What is value of (cos70°/sin20°) + (cos59°/sin31°) - 8 sin230° ?

What is value of (cos70°/sin20°) + (cos59°/sin31°) - 8 sin230° ? Correct Answer 0

Given

(cos70°/sin20°) + (cos59°/sin31°) - 8 sin230°

Concept

Using 

cos(90° - θ) = sinθ 

sin(90° - θ) = cosθ 

sin30° = (1/2)

Calculation

cos70° = cos(90°  - 20°)

⇒ cos70° = sin20°  and

⇒ cos59° = cos(90° - 31°)

⇒ cos59° = sin31° 

Now, substitute the values in equation

⇒ (sin20°/sin20°) + (sin31°/sin31°) - 8sin²30°

⇒ 1 + 1 - (8 × (1/2)²)

⇒ 2 - (8 × (1/4))

⇒ 2 - 2 = 0 

∴ (cos70°/sin20°) + (cos59°/sin31°) - 8 sin230° = 0

Additional Information

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