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Sir pls solve the following.
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Asked by rsudipto | 05 Jan, 2019, 09:18: AM
answered-by-expert Expert Answer
sin to the power of 5 x minus cos to the power of 5 x equals fraction numerator 1 over denominator cos space x end fraction minus fraction numerator 1 over denominator sin space x end fraction rightwards double arrow left parenthesis sin squared x right parenthesis squared sin space x minus left parenthesis cos squared x right parenthesis squared space cos space x equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow left parenthesis 1 minus cos squared x right parenthesis squared sin space x minus left parenthesis 1 minus sin squared x right parenthesis squared space cos space x equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow left parenthesis 1 plus cos to the power of 4 x negative 2 cos squared x right parenthesis sin space x minus left parenthesis 1 plus sin to the power of 4 x minus 2 sin squared x right parenthesis space cos space x equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow sin space x plus cos to the power of 4 x space sin space x minus 2 cos squared x sin space x minus cos space x minus sin to the power of 4 x space cos space x plus 2 sin squared x space cos space x equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow sin space x minus space cos space x plus sin space x space cos space x space left parenthesis cos cubed x minus space sin cubed x right parenthesis space plus space 2 cos space x space sin space x left parenthesis sin space x minus cos space x right parenthesis equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow sin space x minus space cos space x plus sin space x space cos space x space left parenthesis cos space x minus space sin space x right parenthesis left parenthesis cos squared x plus sin squared x plus sin space x space cos space x right parenthesis space plus space 2 cos space x space sin space x left parenthesis sin space x minus cos space x right parenthesis equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow sin space x minus space cos space x minus space sin space x space cos space x space left parenthesis sin space x minus space cos space x right parenthesis left parenthesis cos squared x plus sin squared x plus sin space x space cos space x right parenthesis space plus space 2 cos space x space sin space x left parenthesis sin space x minus cos space x right parenthesis equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow left parenthesis sin space x minus space cos space x right parenthesis left square bracket 1 minus space sin space x space cos space x space left parenthesis 1 plus sin space x space cos space x right parenthesis space plus space 2 cos space x space sin space x right square bracket equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow 1 minus space sin space x space cos space x space left parenthesis 1 plus sin space x space cos space x right parenthesis space plus space 2 cos space x space sin space x equals fraction numerator 1 over denominator sin space x space cos space x end fraction rightwards double arrow 1 minus space sin space x space cos space x space left square bracket left parenthesis 1 plus sin space x space cos space x right parenthesis space minus space 2 right square bracket equals fraction numerator 1 over denominator sin space x space cos space x end fraction rightwards double arrow 1 minus space sin space x space cos space x space left square bracket sin space x space cos space x space minus space 1 right square bracket equals fraction numerator 1 over denominator sin space x space cos space x end fraction rightwards double arrow sin space x space cos space x space left square bracket sin space x space cos space x space minus space 1 right square bracket equals 1 minus fraction numerator 1 over denominator sin space x space cos space x end fraction rightwards double arrow sin space x space cos space x space left square bracket sin space x space cos space x space minus space 1 right square bracket equals fraction numerator sin space x space cos space x minus 1 over denominator sin space x space cos space x end fraction rightwards double arrow sin squared x space cos squared x space equals 1 rightwards double arrow sin squared x space equals fraction numerator 1 over denominator cos squared x end fraction S i n c e comma space sin space x element of left square bracket negative 1 comma 1 right square bracket space rightwards double arrow sin squared x element of left square bracket 0 comma 1 right square bracket rightwards double arrow fraction numerator 1 over denominator cos squared x end fraction element of left square bracket 0 comma 1 right square bracket space w h i c h space i s space n o t space t r u e. T h u s comma space t h e space g i v e n space e q u a t i o n space h a s space n o space s o l u t i o n. H e n c e comma space z e r o space s o l u t i o n.sin to the power of 5 x minus cos to the power of 5 x equals fraction numerator 1 over denominator cos space x end fraction minus fraction numerator 1 over denominator sin space x end fraction rightwards double arrow left parenthesis sin squared x right parenthesis squared sin space x minus left parenthesis cos squared x right parenthesis squared space cos space x equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow left parenthesis 1 minus cos squared x right parenthesis squared sin space x minus left parenthesis 1 minus sin squared x right parenthesis squared space cos space x equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow left parenthesis 1 plus cos to the power of 4 x negative 2 cos squared x right parenthesis sin space x minus left parenthesis 1 plus sin to the power of 4 x minus 2 sin squared x right parenthesis space cos space x equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow sin space x plus cos to the power of 4 x space sin space x minus 2 cos squared x sin space x minus cos space x minus sin to the power of 4 x space cos space x plus 2 sin squared x space cos space x equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow sin space x minus space cos space x plus sin space x space cos space x space left parenthesis cos cubed x minus space sin cubed x right parenthesis space plus space 2 cos space x space sin space x left parenthesis sin space x minus cos space x right parenthesis equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow sin space x minus space cos space x plus sin space x space cos space x space left parenthesis cos space x minus space sin space x right parenthesis left parenthesis cos squared x plus sin squared x plus sin space x space cos space x right parenthesis space plus space 2 cos space x space sin space x left parenthesis sin space x minus cos space x right parenthesis equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow sin space x minus space cos space x minus space sin space x space cos space x space left parenthesis sin space x minus space cos space x right parenthesis left parenthesis cos squared x plus sin squared x plus sin space x space cos space x right parenthesis space plus space 2 cos space x space sin space x left parenthesis sin space x minus cos space x right parenthesis equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow left parenthesis sin space x minus space cos space x right parenthesis left square bracket 1 minus space sin space x space cos space x space left parenthesis 1 plus sin space x space cos space x right parenthesis space plus space 2 cos space x space sin space x right square bracket equals fraction numerator sin space x minus cos space x over denominator sin space x space cos space x end fraction rightwards double arrow 1 minus space sin space x space cos space x space left parenthesis 1 plus sin space x space cos space x right parenthesis space plus space 2 cos space x space sin space x equals fraction numerator 1 over denominator sin space x space cos space x end fraction rightwards double arrow 1 minus space sin space x space cos space x space left square bracket left parenthesis 1 plus sin space x space cos space x right parenthesis space minus space 2 right square bracket equals fraction numerator 1 over denominator sin space x space cos space x end fraction rightwards double arrow 1 minus space sin space x space cos space x space left square bracket sin space x space cos space x space minus space 1 right square bracket equals fraction numerator 1 over denominator sin space x space cos space x end fraction rightwards double arrow sin space x space cos space x space left square bracket sin space x space cos space x space minus space 1 right square bracket equals 1 minus fraction numerator 1 over denominator sin space x space cos space x end fraction rightwards double arrow sin space x space cos space x space left square bracket sin space x space cos space x space minus space 1 right square bracket equals fraction numerator sin space x space cos space x minus 1 over denominator sin space x space cos space x end fraction rightwards double arrow sin squared x space cos squared x space equals 1 rightwards double arrow sin squared x space equals fraction numerator 1 over denominator cos squared x end fraction S i n c e comma space sin space x element of left square bracket negative 1 comma 1 right square bracket space rightwards double arrow sin squared x element of left square bracket 0 comma 1 right square bracket rightwards double arrow fraction numerator 1 over denominator cos squared x end fraction element of left square bracket 0 comma 1 right square bracket space w h i c h space i s space n o t space t r u e. T h u s comma space t h e space g i v e n space e q u a t i o n space h a s space n o space s o l u t i o n. H e n c e comma space z e r o space s o l u t i o n. Answered by Yasmeen Khan | 14 Jan, 2019, 16:06: PM

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