If sin 10θ = cos8θ and 10θ is a positive acute angle, then find the value of tan9θ. ( WBBSE – 2019 )

If sin 10θ = cos8θ and 10θ is a positive acute angle, then find the value of tan9θ.

Solution :

sin 10θ = cos8θ [ ∵ sin ( 90 – θ ) = cos = θ ]

⇒ sin 10θ = sin ( 90 – 8θ )

⇒ 10θ = 90- 8θ

⇒ 10Θθ + 8θ = 90

⇒ 18θ = 90

⇒ θ = 90 / 18

⇒ θ = 5

Now, tan 9θ = tan ( 9 × 5)

= tan 45°

= 1