Is (cos(3x))/(cos(x))=1-4sin^2(x) ?

The answer to whether (cos(3x))/(cos(x))=1-4sin^2(x) is True

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prove (cos(3x))/(cos(x))=1-4sin^2(x)

prove

\frac{cos ( 3 x )}{cos ( x )} = 1 - 4 sin^{2} (x)

True

Solution steps

\frac{cos ( 3 x )}{cos ( x )} = 1 - 4 sin^{2} (x)

Manipulating left side

\frac{cos ( 3 x )}{cos ( x )}

Rewrite using trig identities

= - 4 sin^{2} (x) + 1

= 1 - 4 sin^{2} (x)

We showed that the two sides could take the same form

\Rightarrow True

cos (- 2 π)

sin (θ) = cos (θ)

cot (θ) - 1 = 0

2 sin (θ) - 2 = 0

sin (\frac{3 π}{4})

Is (cos(3x))/(cos(x))=1-4sin^2(x) ?
The answer to whether (cos(3x))/(cos(x))=1-4sin^2(x) is True