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