For what value of t is the value of sin2t, half of the value of tan(t)?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 60°.
sin2t = (1/2) × tan(t)
⇒ 2sin(t)cos(t) = (1/2) × [sin(t)/cos(t)]
⇒ 4sin(t)cos2(t) = sin(t)
⇒ 4cos2(t) = 1
⇒ cos2(t) = 1/4
⇒ cos(t) = √(1/4) = 1/2 = cos 60°
⇒ t = 60°
Therefore, the value of t is 60°.