Question

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

Answer 1

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

Answer 2

Heya !!


Sin²15 + Sin75 / Cos²36 + Cos²54



=> Sin²(90 - 75 ) + Sin²75 / Cos²(90-54) + Cos²54





=> Cos²75 + Sin²75 / Sin²54 + Cos²54




=> (Sin²75 + Cos²75) / ( Sin²75 + Cos²75)






=> 1