Q12 of 268 Page 4

If sec 5 θ =cosec (θ -36^o), where 5 θ is an acute angle, find the value of θ.

sec 5θ = cosec (θ-36°) …(i)

We know that

sec θ = cosec (90° - θ)

So, Eq. (i) become

Cosec (90° - 5θ) = cosec (θ -36°)

On Equating both the sides, we get

90° - 5θ = θ -36°

⇒ -5θ - θ = -36° -90°

⇒ -6θ = -126°

⇒ θ = 21°

Find θ if cos(2 θ +54^o)= sin θ, where (2θ +54^o) is an acute angle.

If tan 3 θ =cot (θ +18^o), where 3 θ and θ +18^o are acute angles, find the value of θ.

Prove that :

sin 70^o. sec 20^o=1

Prove that :

sin (90^o- θ) tan θ=sin θ

If sec 5 θ =cosec (θ -36o), where 5 θ is an acute angle, find the value of θ.