Question

Find the value of theta, if
cos theta
1-sin theta
cos theta
1 - sin
=4, theta =90°or less than 90​

Answer 1

Step-by-step explanation:

Okay. We've got:

cosθ1−sinθ+cosθ1+sinθ=4

Let's ignore the RHS for now.

cosθ1−sinθ+cosθ1+sinθ

cosθ(1+sinθ)+cosθ(1−sinθ)(1−sinθ)(1+sinθ)

cosθ((1−sinθ)+(1+sinθ))1−sin2θ

cosθ(1−sinθ+1+sinθ)1−sin2θ

2cosθ1−sin2θ

According to the Pythagorean Identity,

sin2θ+cos2θ=1. So:

cos2θ=1−sin2θ

Now that we know that, we can write: