Question

If sin 2theta = cos 4theta then theta is equal to a) 18 b)15 c)45 D)45​

Answer 1

Answer:

The solution is θ is equal to (b) 15

Step-by-step explanation:

We know that, cos 2θ = 1 - 2sin²θ => cos 4θ = 1 - 2sin²2θ

sin 2θ = cos 4θ

=> sin 2θ = 1 - 2sin²2θ

=> 2sin²2θ + sin 2θ - 1 = 0

=> (2sin 2θ -1)(sin 2θ + 1) = 0

Then, either, sin 2θ + 1 = 0 => sin 2θ= -1 => 2θ = 270° =>2sin 2θ θ = 135°

Or, 2sin 2θ - 1 = 0 => 2sin 2θ = 1 => sin 2θ = 1/2 => sin 2θ = sin 30° => 2θ = 30° => θ = 15°

Hence, θ = 15°