Question

The value of cos 12° + cos 84° + cos 156° + cos 132° is ______.

विकल्प

• `1/2`

• 1

• `(-1)/2`

• `1/8`

Answer 1

The value of cos 12° + cos 84° + cos 156° + cos 132° is `underlinebb((-1)/2)`.

Explanation:

We have,

cos 12° + cos 84° + cos 156° + cos 132° 

= (cos 12° + cos 132°) + (cos 84° + cos 156°) 

= 2 cos 72° cos 60° + 2 cos 120° cos 36°   ...`[∵ cos x + cos y = 2 cos ((x + y)/2) cos((x - y)/2)]`

= `2 xx 1/2 cos 72^circ +  2((-1)/2) cos 36^circ`

= cos 72° – cos 36° 

= cos (90° – 18°) – cos 36°

= sin 18° – cos 36°

= `((sqrt(5) - 1)/4) - ((sqrt(5) + 1)/4)`  ...`[∵ sin18^circ = (sqrt(5) - 1)/4, cos 36^circ = (sqrt(5) + 1)/4]`

= `(sqrt(5) - 1 - sqrt(5) - 1)/4`

= `(-2)/4`

= `(-1)/2`