Question

Evaluate :-
\sf \dfrac{ {sin}^{2} 63 + {sin}^{2}27 }{cos {}^{2} 17 + {cos}^{2} 73}​

Answer 1

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Evaluate :-

$\sf \dfrac{ {sin}^{2} 63 + {sin}^{2}27 }{cos {}^{2} 17 + {cos}^{2} 73}$

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$\frac{ { \sin }^{2}63 + { \sin }^{2}27 }{ { \cos }^{2} 17 + { \cos }^{2}73 } \\ \\ \frac{ \sin^{2}63 + { \sin}^{2}72 }{ \cos^{2} 17 + { \cos }^{2} 73 } \\ \\ \frac{ \sin ^{2} (90 - 27) + { \sin }^{2}27 }{ { \cos }^{2} (90 - 73) + ( { \cos }^{2} 73)} \\ \\ \frac{ { \cos }^{2}27 + { \sin}^{2} 27 }{ { \sin }^{2}73 + { \cos}^{2} 73 } \\ \\ = \frac{1}{1} \\ \\ = 1$

Hence,

$\frac{ { \sin}^{2} 65 + { \sin }^{2}27 }{ { \sin }^{2}17 + { \sin }^{2} 73} = 1$

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