Question

If cos 5θ = sin θ and 5θ < 90°, then the value of tan 3θ is ______.

Answer 1

If cos 5θ = sin θ and 5θ < 90°, then the value of tan 3θ is 1.

Explanation:

cos 5θ = sin θ = cos (90° – θ). 

So cos 5θ = cos (90° – θ) gives 5θ = 90° – θ + 360°k or 5θ = –(90° – θ) + 360°k. 

From the first: 6θ = 90° + 360°k ⇒ θ = 15° + 60°k.

With 5θ < 90° the only admissible value is θ = 15° (k = 0). 

Hence tan 3θ = tan (45°) = 1.