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

Answer:

Step-by-step explanation:

4 cos²x=3

cos²x=3/4

cosx=√3/2

i) x= 30°

ii) cos² x + cot² x

=cos² 30° + cot² 30° = 3/4 + 3 = 15/4

iii) cos 3x

=cos 3x = 4 cos³ x + 3cosx

=4 cos³30°+ 3cos30° = 4×3√3/8 + 3×√3/2

=3√3

(iv) sin 2x​

= sin 2x​= 2 sin x cos x = 2×1/2×√3/2 = √3/2