Question

Find the value of x in the following: `sqrt(3)`tan 2x = cos60° + sin45° cos45°

Answer 1

`sqrt(3)`tan2x = cos60° + sin45° cos45°

⇒ `sqrt(3)tan2x = (1)/(2) + (1)/sqrt(2) xx (1)/sqrt(2)`

⇒`sqrt(3)tan2x = (1)/(2) + (1)/(2)`
⇒`sqrt(3)`tan2x =1

⇒ tan2x = `(1)/sqrt(3)`
⇒ tan2x = tan30°
⇒ 2x = 30°
⇒ x = 15°.