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CBSE Class 7 Answered

prove that the function is a periodic function 
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Asked by yashasvi0602 | 03 Jun, 2020, 11:40: PM
answered-by-expert Expert Answer
f(x) = sin2x/(sin4x + cos4x) = sin2x/{1-(sin22x)/2}
sin 2x is periodic with period pi
sin22x is periodic with period pi/2
sin22x will also be periodic with period pi
We know that if f(x) and g(x) are periodic with period T then f(x)/g(x) will also be periodic with period T.
Therefore, sin2x/{1-(sin22x)/2} is periodic with period pi
i.e., f(x) is periodic with period pi

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T h e r e f o r e comma space w e space h a v e
integral subscript straight pi superscript fraction numerator 5 straight pi over denominator 4 end fraction end superscript fraction numerator sin space 2 x over denominator sin to the power of 4 x plus cos to the power of 4 x end fraction d x equals integral subscript straight pi superscript straight pi plus straight pi over 4 end superscript fraction numerator sin space 2 x over denominator sin to the power of 4 x plus cos to the power of 4 x end fraction d x
equals integral subscript 0 superscript straight pi fraction numerator sin space 2 x over denominator sin to the power of 4 x plus cos to the power of 4 x end fraction d x
equals integral subscript 0 superscript straight pi fraction numerator sin space 2 x over denominator 1 minus begin display style fraction numerator sin squared 2 x over denominator 2 end fraction end style end fraction d x
N o w space s o l v e space t h i s space t o space g e t space t h e space v a l u e space o f space t h e space i n t e g r a l.
 
 
 
Note: This question does not belong to your syllabus, it belongs to class 11-12. This you will be learning in class 11.
Answered by Renu Varma | 04 Jun, 2020, 11:17: AM
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