Question

Find the value of x in the following: cos2x = cos60° cos30° + sin60° sin30°

Answer 1

cos2x = cos60° cos30° + sin60° sin30°

⇒ cos2x = `(1)/(2) xx sqrt(3)/(2) + sqrt(3)/(2) xx (1)/(2)`

⇒ cos2x = `sqrt(3)/(4) + sqrt(3)/(4)`

⇒ cos2x = `(2sqrt(3))/(4)`

⇒ cos2x = `sqrt(3)/(2)`
⇒ cos2x = cos30°
⇒ 2x = 30°
⇒ x = 15°.