1.

Sin square 15 plus sin square 75/cos square 36 plus cos square 54

Answer»
\frac{ \sin^{2} (15) + \sin^{2} (75) }{ \cos ^{2} (36) + \cos ^{2} (54) } \\ \\ \\ => \frac{ \sin ^{2} (90 - 75) + \sin^{2} (75) }{ \cos ^{2} (90 - 54) + \cos^{2} (54) } \\ \\ \\ \\ => \frac{ \cos^{2} (75) + \sin^{2} (75) }{ \sin^{2} (54) + \cos^{2} (54) } \\ \\ \\ \\ \mathbf{ \textcolor{blue}{we \: \: know \: \: \: ( \: \: \: \: \: \sin ^{2} ( \theta) \: + \: \cos ^{2} ( \theta ) = 1 \: \: \: \: \: )}} \\ \\ \\ \\ \\ hence \\ \\ \rightarrow \frac{1}{1} \\ \\ \rightarrow1


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