Question

Cos^2 49+cos^2 41/sin^2 31+sin^2 59+2tan35 tan55

Answer 1

Numerator

cos² 49 + cos² 41

⇒cos² 49 + cos² ( 90 - 49)

[ cos (90 - x) = sin x]

⇒cos² 49 + sin² 49 = 1

By Trigonometry identity

sin²x + cos²x = 1

Denominator

⇒sin² 31 + sin² 59 + 2 tan35. tan 55

⇒sin² 31 + sin² ( 90 - 31) + 2 tan(90-55). tan55

⇒sin² 31 + cos² 31 + 2 cot55. tan55

⇒ 1 + 2 ( 1)

⇒ 3

By Trigonometry identity

sin²x + cos²x = 1,

tanx. cot x = 1

Therefore, The required answer is 1/3.