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

Question

$3sin^2θ-cos^2θ-1$

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Answer 1 · 2018-05-17T03:45:10

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

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:

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