CBSE Class 11-science Answered

Solve for x 3tanx + cotx = 5cosecx

Asked by dssinghania1234 | 27 Oct, 2018, 10:20: AM

Expert Answer

3 space tan x plus c o t space x equals 5 cos e c space x 3 fraction numerator sin x over denominator cos x end fraction plus space fraction numerator cos space x over denominator sin space x end fraction equals fraction numerator 5 over denominator sin space x end fraction fraction numerator 3 space sin squared x plus cos squared x over denominator cos space x space sin space x end fraction equals fraction numerator 5 over denominator sin space x end fraction fraction numerator 2 space sin squared x plus sin to the power of 2 space end exponent x plus cos squared x over denominator cos space x space sin space x end fraction equals fraction numerator 5 over denominator sin space x end fraction fraction numerator 2 space sin squared x plus space 1 over denominator cos space x space sin space x end fraction equals fraction numerator 5 over denominator sin space x end fraction 2 sin cubed x space plus sin x equals 5 sin x space cos x 2 sin cubed x space plus sin x minus 5 sin x space cos x equals 0 sin x space left parenthesis 2 space sin squared x minus 5 cos x space plus 1 right parenthesis space equals 0 s o space sin x equals 0 space O R space space 2 space sin squared x minus 5 cos x space plus 1 equals 0 s o space x equals space n pi space space O R space space 2 space left parenthesis 1 minus cos squared x right parenthesis minus 5 space cos x space plus 1 equals 0 2 minus 2 cos squared x minus 5 space cos x space plus 1 equals 0 2 cos squared x plus 5 space cos x space minus 3 equals 0 2 cos squared space x plus space 6 space cos space x minus cos space x space minus 3 equals 0 2 cos x left parenthesis space cos x plus 3 right parenthesis minus 1 left parenthesis cos space x plus 3 right parenthesis space equals 0 left parenthesis 2 space cos x minus 1 right parenthesis left parenthesis cos space x plus 3 right parenthesis equals 0 cos space x equals 1 half space o r space cos space x space equals 3 sin c e space cos space x equals 3 space n o t space p o s s i b l e space space left parenthesis negative 1 less or equal than cos x less or equal than 1 right parenthesis cos space x equals 1 half cos x space equals space cos left parenthesis pi over 3 right parenthesis h e n c e space x equals 2 n pi plus-or-minus pi over 3 h e n c d e space x equals n pi space o r space x equals 2 n pi plus-or-minus pi over 3

b u t space x equals n pi space e q u a t i o n space n o t space s a t i s f y space sin c e space c o t space x space i s space u n d e f i n e d space s o space x equals 2 n pi plus-or-minus pi over 3

Answered by Ram Singh | 28 Oct, 2018, 04:05: PM

CBSE Class 11-science Answered

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CBSE Class 11-science Answered

Concept Videos

General and principal solutions of trigonometric equati ...

Distinguish between general and principal solutions ...

Trigonometric Equations

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