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Maths-

General

Easy

Question

$sin to the power of 4 space pi over 16 plus sin to the power of 4 fraction numerator 3 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 5 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 7 pi over denominator 16 end fraction$

1
1/2
3/2
2

hint Hint:

In the question we will first use the formula $sin straight pi over 2 minus theta equals cos theta$ then we will simplify the equation using other trigonometric identities.

The correct answer is: 3/2

$sin to the power of 4 space pi over 16 plus sin to the power of 4 fraction numerator 3 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 5 pi over denominator 16 end fraction plus sin to the power of 4 space fraction numerator 7 pi over denominator 16 end fraction equals sin to the power of 4 straight pi over 16 plus sin to the power of 4 open parentheses straight pi over 2 minus straight pi over 16 close parentheses plus sin to the power of 4 fraction numerator 3 straight pi over denominator 16 end fraction plus sin to the power of 4 open parentheses straight pi over 2 minus fraction numerator 3 straight pi over denominator 16 end fraction close parentheses space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals sin to the power of 4 straight pi over 16 plus cos to the power of 4 straight pi over 16 plus sin to the power of 4 fraction numerator 3 straight pi over denominator 16 end fraction plus cos to the power of 4 fraction numerator 3 straight pi over denominator 16 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets sin open parentheses straight pi over 2 minus A close parentheses equals cos A close square brackets equals open parentheses sin squared straight pi over 16 plus cos squared straight pi over 16 close parentheses squared minus 2 sin squared straight pi over 16 cos squared straight pi over 16 plus open parentheses sin squared fraction numerator 3 straight pi over denominator 16 end fraction plus cos squared fraction numerator 3 straight pi over denominator 16 end fraction close parentheses squared minus 2 sin squared fraction numerator 3 straight pi over denominator 16 end fraction cos squared fraction numerator 3 straight pi over denominator 16 end fraction space space space space space equals 1 minus 1 half sin squared straight pi over 8 plus 1 minus 1 half sin squared fraction numerator 3 straight pi over denominator 8 end fraction space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets 4 sin squared A. cos squared A equals sin squared 2 A close square brackets equals 2 minus 1 half open square brackets sin squared straight pi over 8 plus sin squared fraction numerator 3 straight pi over denominator 8 end fraction close square brackets equals 2 minus 1 half open square brackets sin squared straight pi over 8 plus sin squared open parentheses straight pi over 2 minus straight pi over 8 close parentheses close square brackets equals 2 minus 1 half open square brackets sin squared straight pi over 8 plus cos squared straight pi over 8 close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open square brackets sin open parentheses straight pi over 2 minus A close parentheses equals cos A close square brackets equals 2 minus 1 half equals 3 over 2$

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