Q12 of 268 Page 4

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

cos(2 θ +54^o)= sin θ …(i)

We know that

Sin θ = cos (90° - θ)

So, Eq. (i) become

cos(2 θ +54^o) = cos( 90° - θ)

On Equating both the sides, we get

2θ + 54° = 90° - θ

⇒ 2θ + θ = 90° - 54°

⇒ 3θ = 36°

⇒ θ = 12°

In a ∆ABC prove that

If sin 3A = cos(A – 26^o), where 3A is an acute angle, find the value of A.

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

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

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