Question

Find the value  of x in the following :

(i) cos x = cos 60° cos 30° + sin 60° sin 30°

(ii) sin 2x = sin 60° cos 30° – cos 60° sin 30°

(iii) √3 tan2x = sin 30° + sin 45° cos 45° + 2 sin 90°.

Answer 1

(i) cos x = cos 60° cos 30° + sin 60° sin 30°

cos x = cos 30°

x = 30°

(ii) sin 2x = sin 60° cos 30° – cos 60° sin 30°

⇒ sin 2x = 1/2 = sin 30°

⇒ 2x = 30° ⇒ x = 15°

(iii) √3 tan2x = sin 30° + sin 45° cos 45° + 2 sin 90°.

√3 tan2x = 3

⇒ tan 2x = 3/√3

⇒ tan 2x = √3

⇒ tan 2x = tan 60°

⇒ 2x = 60°

⇒ x = 30°