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Maths-

General

Easy

Question

$open parentheses sin to the power of 8 space 75 to the power of ring operator minus cos to the power of 8 space 75 to the power of ring operator close parentheses$ =

$\frac{7 \sqrt{3}}{8}$
$\frac{3 \sqrt{3}}{8}$
$\frac{3 \sqrt{3}}{16}$
$\frac{7 \sqrt{3}}{16}$

hint Hint:

In this question, we have to find the value of the given equation. For that we will simplify the equation using some trigonometric identities and later substitute the value to get the required value.

The correct answer is: $fraction numerator 7 square root of 3 over denominator 16 end fraction$

$space space space open parentheses sin to the power of 8 space 75 to the power of ring operator minus cos to the power of 8 space 75 to the power of ring operator close parentheses equals sin to the power of 8 open parentheses 90 minus 15 close parentheses degree minus cos to the power of 8 left parenthesis 90 minus 15 right parenthesis degree equals cos to the power of 8 15 degree minus sin to the power of 8 15 degree equals open parentheses cos to the power of 4 15 degree plus sin to the power of 4 15 degree close parentheses open parentheses cos to the power of 4 15 degree minus sin to the power of 4 15 degree close parentheses equals open parentheses open parentheses cos squared 15 degree plus sin squared 15 degree close parentheses squared minus 2 sin squared 15 degree. cos squared space 15 degree close parentheses open parentheses cos squared 15 degree plus sin squared 15 degree close parentheses open parentheses cos squared 15 degree minus sin squared 15 degree close parentheses equals open parentheses 1 minus open parentheses 2 sin space 15 degree. cos 15 degree close parentheses squared over 2 close parentheses 1 cross times cos open parentheses 2 cross times 15 close parentheses degree equals open parentheses 1 minus fraction numerator s i n squared 30 degree over denominator 2 end fraction close parentheses cos space 30 degree equals open parentheses 1 minus 1 over 8 close parentheses fraction numerator square root of 3 over denominator 2 end fraction equals 7 over 8. fraction numerator square root of 3 over denominator 2 end fraction equals fraction numerator 7 square root of 3 over denominator 16 end fraction$

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