What is value of (cos77°/sin13°) + (cos69°/sin21°) - 8 sin230° ?

What is value of (cos77°/sin13°) + (cos69°/sin21°) - 8 sin230° ? Correct Answer 0

Given

(cos77°/sin13°) + (cos69°/sin21°) - 8 sin230°

Concept

Using 

cos(90° - θ) = sinθ 

sin(90° - θ) = cosθ 

sin30° = (1/2)

Calculation

cos77° = cos(90°  - 13°)

⇒ cos77° = sin13°  and

⇒ cos69° = cos(90° - 21°)

⇒ cos69° = sin21° 

Now, substitute the values in equation

⇒ (sin13°/sin13°) + (sin21°/sin21°) - 8sin230°

⇒ 1 + 1 - (8 × (1/2)2)

⇒ 2 - (8 × (1/4))

⇒ 2 - 2 = 0 

∴ (cos77°/sin13°) + (cos69°/sin21°) - 8 sin230° = 0