If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ, then 2 sin 3θ – √3 tan 4θ is equal to
Given,
5θ and 4 θ are acute angles,
Therefore,
5θ + 4θ = 90°
9θ = 90°
θ = 90/9 = 10°
Then value of-
2 sin 3θ - √3 tan 3 θ
Putting value of θ = 10°,
We get,
⇒ 2 sin 3(10) - √3 tan 3(10)
⇒ 2 sin 30° - √3 tan 30° [∵ sin 30° = 1/2 and tan 30° = 1/√3]
⇒ 2× 1/2 - √3 x
⇒ 1 – 1 = 0