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Maths-

General

Easy

Question

If $f left parenthesis x right parenthesis equals sin squared space open parentheses pi over 8 plus x over 2 close parentheses minus sin squared space open parentheses pi over 8 minus x over 2 close parentheses$ , then the period of f(x) is

$π$
$\frac{π}{2}$
$\frac{π}{3}$
$2 π$

hint Hint:

In the question we have to find the fundamental period of the given equation. For this we will first simplify the given equation using some trigonometric identities then by using periodic functions we can find the required result.

The correct answer is: $2 pi$

$f left parenthesis x right parenthesis equals sin squared space open parentheses pi over 8 plus x over 2 close parentheses minus sin squared space open parentheses straight pi over 8 minus x over 2 close parentheses equals 1 half open square brackets 1 minus cos 2 open parentheses straight pi over 8 plus x over 2 close parentheses space close square brackets minus 1 half open square brackets 1 minus cos 2 open parentheses straight pi over 8 minus x over 2 close parentheses close square brackets equals 1 half open square brackets 1 minus cos open parentheses straight pi over 4 plus x close parentheses space close square brackets minus 1 half open square brackets 1 minus cos open parentheses straight pi over 4 minus x close parentheses close square brackets equals 1 half open square brackets cos open parentheses straight pi over 4 minus x close parentheses minus cos open parentheses straight pi over 4 plus x close parentheses close square brackets equals 1 half open square brackets cos straight pi over 4. cos x space plus sin straight pi over 4 sin x space minus cos straight pi over 4 cos x plus sin straight pi over 4 sin x close square brackets equals 1 half open square brackets 2 sin straight pi over 4 sin x close square brackets equals fraction numerator 1 over denominator square root of 2 end fraction sin x space f u n d a m e n t a l space p e r i o d space o f space sin a x space i s space fraction numerator 2 straight pi over denominator a end fraction. S o comma space p e r i o d space o f space fraction numerator 1 over denominator square root of 2 end fraction sin x equals 2 straight pi$

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