Question

If 4 cos² x = 3 and x is an acute angle;
find the value of :
(i) x 
(ii) cos² x + cot² x
(iii) cos 3x (iv) sin 2x

Answer 1

(i) 4 cos²x = 3

cos²x = `(3)/(4)`

cos x = `(sqrt3)/(2)`

x = 30°

(ii) cos²x + cot²x = cos²30° + cot²30°

 = `(3)/(4) + 3`

= `(15)/(4)`

= 3`(3)/(4)`

(iii) cos 3x = cos3(30°) = cos 90° = 0

(iv) sin 2x = sin 2(30°) = sin60° = `(sqrt3)/(2)`