cos2 𝜃1+sin 𝜃 = 1 − sin 𝜃

The given equation is cos^2 𝜃 + sin 𝜃 = 1 - sin 𝜃.

Step 1: We know that cos^2 𝜃 = 1 - sin^2 𝜃 (from the Pythagorean identity in trigonometry). So, we can replace cos^2 𝜃 in the equation.

So, the equation becomes 1 - sin^2 𝜃 + sin 𝜃 = 1 - sin 𝜃.

Step 2: Simplify the equation by subtracting sin 𝜃 from both sides.

This gives us 1 - sin^2 𝜃 = 1 - 2sin 𝜃.

Step 3: Rearrange the equation to make it a quadratic equation in terms of sin 𝜃.

This gives us sin^2 𝜃 + 2sin 𝜃 - 1 = 0.

Step 4: Solve this quadratic equation to find the values of sin 𝜃.

This can be done either by factoring, completing the square, or using the quadratic formula. The solutions will give you the possible values of 𝜃.