Question

evaluate and justify : sin square 15 + sin square 75 / cos square 36 + cos square 54

Answer 1

$\frac{ \sin ^{2} (15 ) + \sin^{2} (75) }{ \cos^{2} (36) + \cos ^{2} (54) } \\ \\ \\ \\ \frac{ \sin ^{2} (90 - 75 ) + \sin^{2} (75) }{ \cos ^{2} (90 - 54) + \cos ^{2} (54) } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \bold{ | \: \sin ^{2} (90 - \theta) = \cos( \theta) \: \: \: \: \: \: and \: \: \: \: \: \: \cos^{2} (90 - \theta) = \sin ^{2} ( \theta) } \\ \\ \\ \\ \frac{ \cos ^{2} (75) + \sin^{2} (75) }{ \sin^{2} (54) + \cos ^{2} (54) } \: \: \: \: \: \: \: \: \: \: | \bold{ \: \sin ^{2} (a) + \cos^{2} (a) = 1} \\ \\ \\ \\ \frac{1}{1} \\ \\ \\ \\ 1$

Answer 2

Sin² 15° + Sin²75° / Cos²36° + Cos²54°



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




=> Cos²75° + Sin² 75° / Sin²54° + Cos²54° .




=> Sin² 75° + Cos²75° / Sin²54° + Cos²54°




=> 1/1


=> 1