Correct Answer - Option 3 : 20°
Given:
The given expression is 2cot3x = sin60° + (1/2) sin30°.sec30°
Formula Used:
Basic concept of trigonometric ratio and identities
We know that
Sin60° = √3/2, Sin30° = ½, cot 60° = 1/√3 and sec30° = 2/√3
Calculation:
By putting the value of trigonometric angles in the expression
∴ 2cot3x = √3/2 + 1/2 × 1/2 × 2/√3
⇒ 2cot3x = √3/2 + 2/4√3
⇒ 2cot3x = 4/2√3
⇒ cot3x = 1/√3
We know that cot60° = 1/√3
∴ cot3x = cot 60°
⇒ 3x = 60°
⇒ x = 20°
Hence, option (3) is correct
