CBSE Class 7 Answered

prove that the function is a periodic function

Asked by yashasvi0602 | 03 Jun, 2020, 11:40: PM

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

integral subscript a superscript a plus T end superscript f open parentheses x close parentheses d x equals integral subscript 0 superscript T f open parentheses x close parentheses d x comma space space w h e r e space T space i s space t h e space p e r i o d space o f space f left parenthesis x right parenthesis 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

Concept Videos