Is this possible to factor? 3sin^2θ-cos^2θ-1

3sin^2θ-cos^2θ-1

1 Answer
May 17, 2018

Not in its current form but a substitution makes it factorable as the difference of two squares.

Explanation:

Given 3sin^2(theta)-cos^2(theta)-1

Substitute cos^2(theta) = 1- sin^2(theta)

3sin^2(theta)-(1-sin^2(theta))-1

Distribute the minus:

3sin^2(theta)-1+sin^2(theta))-1

Combine like terms:

4sin^2(theta)-2

The above factors as the difference of two squares:

(2sin(theta)-sqrt2)(2sin(theta)+sqrt2)