Factor sin(x)-cos(x)^2-1

Problem

sin(x)−cos2(x)−1

Solution

1. Use the Pythagorean identity to rewrite cos2(x) in terms of sin(x) so that the expression contains only one trigonometric function.

cos2(x)=1−sin2(x)

2. Substitute the identity into the original expression.

sin(x)−(1−sin2(x))−1

3. Distribute the negative sign and combine like terms to simplify the expression into a standard quadratic form.

sin(x)−1+sin2(x)−1

sin2(x)+sin(x)−2

4. Factor the quadratic expression by finding two numbers that multiply to −2 and add to 1 These numbers are 2 and −1

(sin(x)+2)*(sin(x)−1)

Final Answer

sin(x)−cos2(x)−1=(sin(x)+2)*(sin(x)−1)

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