Question

If 5θ and 4θ are acute angles satisfying sin 5θ = cos 4θ, then 2 sin 3θ −\[\sqrt{3} \tan 3\theta\]  is equal to 

Options

•  1

•  0

•  −1

• \[1 + \sqrt{3}\]

Answer 1

We are given that 5θ and 4θ are acute angles satisfying the following condition sin 5θ = cos 4θ. We are asked to find 2 `sin 3θ -sqrt3 tan 3θ `

⇒ `sin 5θ= cos 4θ`

⇒` cos (90°-5θ)= cos 4θ` 

⇒` 90°-5θ=4θ` 

⇒ `90=90°` 

Where `5θ` and `4θ` are acute angles 

⇒ `θ=10°`

Now we have to find: 

 `2 sin 3θ-sqrt3 tan 3θ` 

=` 2 sin 30°-sqrt3 tan 30°` 

= `2xx1/2-sqrt3xx1/sqrt3`

=`1-1`

=` 0`