Question

Find the value of: cos²20°+cos²70°/sin²59°+sin²31°.

Answer 1

Two angles are said to be complementary of their sum is equal to 90° .
θ & (90° - θ) are complementary angles
SOLUTION:

GIVEN:
cos²20°+cos²70°/sin²59°+sin²31°
= cos² 20° + cos² (90° - 20°) / sin²59°+sin² (90° - 59°)
= cos² 20° + sin² 20° / sin²59°+ cos² 59°

[cos (90 - θ) = sin θ , sin (90 - θ ) = cos θ]
= 1/1

[ sin² θ + cos² θ = 1]

cos²20°+cos²70°/sin²59°+sin²31° = 1

Hence, the value of cos²20°+cos²70°/sin²59°+sin²31° is 1.

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Answer 2

Here it is.

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