XAT 2023 Question Paper | Quantitative Aptitude and Data Interpretation

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Question 10 : Find the value of: \( \frac{\sin ^6 15^0+\sin ^6 75^0+6 \sin ^2 15^0 \sin ^2 75^0}{\sin ^4 15^0+\sin ^4 75^0+5 \sin ^2 15^0 \sin ^2 75^0} \)

Video Explanation

Explanatory Answer

\( \frac { \sin ^ { 6 } 15 + \sin ^ { 6 } 75 + 6 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } { \sin ^ { 4 } 15 + \sin ^ { 4 } 75 + 5 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } \)
\( \frac { \sin ^ { 6 } 15 + \sin ^ { 6 } 75 + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } { \sin ^ { 4 } 15 + \sin ^ { 4 } 75 + 2 \sin ^ { 2 } 15 \sin ^ { 2 } 75 + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } \)
\( \frac { \sin ^ { 6 } 15 + \cos ^ { 6 } 15 + 3 \sin ^ { 2 } 15 \cos ^ { 2 } 15 + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } { \sin ^ { 4 } 15 + \cos ^ { 4 } 15 + 2 \sin ^ { 2 } 15 \cos ^ { 2 } 15 + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } \)
\( \frac { \sin ^ { 6 } 15 + \cos ^ { 6 } 15 + 3 \sin ^ { 2 } 15 \cos ^ { 2 } 15 \left( \sin ^ { 2 } 15 + \cos ^ { 2 } 15 \right) + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } { \sin ^ { 4 } 15 + \cos ^ { 4 } 15 + 2 \sin ^ { 2 } 15 \cos ^ { 2 } 15 \left( \sin ^ { 2 } 15 + \cos ^ { 2 } 15 \right) + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } \)
\( \frac { \left( \sin ^ { 2 } 15 + \cos ^ { 2 } 15 \right) ^ { 3 } + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } { \left( \sin ^ { 2 } 15 + \cos ^ { 2 } 15 \right) ^ { 2 } + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } \)
\( \frac { ( 1 ) ^ { 3 } + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } { ( 1 ) ^ { 2 } + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } \)
\( \frac { 1 + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } { 1 + 3 \sin ^ { 2 } 15 \sin ^ { 2 } 75 } \)
= 1

The question is " Find the value of: \( \frac{\sin ^6 15^0+\sin ^6 75^0+6 \sin ^2 15^0 \sin ^2 75^0}{\sin ^4 15^0+\sin ^4 75^0+5 \sin ^2 15^0 \sin ^2 75^0} \) "

Hence, the answer is '1'

Choice C is the correct answer.

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