If cos 9∝ =sin∝ and 9∝ <90^{0}, then the value of tan 5∝ is

Given: cos 9∝ = sin ∝ and 9∝<90° i.e. 9α is an acute angle

And we know that, sin(90°-θ) = cos θ by property.

So, we can write cosine in terms of sine using this property,

cos 9∝ = sin (90°-∝)

Thus, sin (90°-9∝) = sin∝ (∵cos 9∝ = sin(90°-9∝) & sin(90°-∝) = sin∝ )

⇒ 90°-9∝ =∝

⇒ 10∝ = 90° (By rearranging)

⇒ ∝ = 9°

We have got the value of ∝ i.e. ∝ = 9°

Putting it in tan 5∝, we get

tan 5∝ = tan (5.9) = tan 45° = 1

∴, tan 5∝ = 1

8