Question

Solve the equation on the interval 0 ≤ θ < 2π.

sin^2 θ - cos^2 θ = 1 + cos θ

Answer 1

Step 1:

The expression is .

Pythagorean identity : .

Substitute in above expression.

Step 2:

Solve for .

The general solution of , then .

Where .

Substitute in .

.

Substitute in .

.

Solution for in the interval , then .

Step 3:

Solve for .

The general solution of , then .

Where .

Substitute in .

.

Substitute in .

.

Solution for in the interval , then .

Solution :

Solution for in the interval , then .