Question

If cos 9α = sinα and 9α < 90°, then the value of tan5α is ______.

Options

• `1/sqrt(3)`

• `sqrt(3)`

• 1

• 0

Answer 1

If cos 9α = sinα and 9α < 90°, then the value of tan5α is 1.

Explanation:

According to the question,

cos 9α = sin α and 9α < 90°

i.e. 9α is an acute angle

We know that,

sin(90° – θ) = cos θ

So, cos 9α = sin(90° – α)

Since, cos 9α = sin(90° – 9α) and sin(90° – α) = sin α

Thus, sin(90° – 9α) = sin α

90° – 9α = α

10α = 90°

α = 9°

Substituting α = 9° in tan 5α, we get,

tan 5α = tan(5 × 9°)

= tan 45°

= 1

∴ tan 5α = 1