Is cos(4θ)=8cos^4(θ)-8cos^2(θ)+1 ?

The answer to whether cos(4θ)=8cos^4(θ)-8cos^2(θ)+1 is True

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prove cos(4θ)=8cos^4(θ)-8cos^2(θ)+1

prove

cos (4 θ) = 8 cos^{4} (θ) - 8 cos^{2} (θ) + 1

True

Solution steps

cos (4 θ) = 8 cos^{4} (θ) - 8 cos^{2} (θ) + 1

Manipulating left side

cos (4 θ)

Rewrite using trig identities

= 8 cos^{4} (θ) - 8 cos^{2} (θ) + 1

We showed that the two sides could take the same form

\Rightarrow True

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

sin (2 A) = 2 sin (A) cos (A)

tan (A - B) = sin (A - B) sec (A - B)

cot^{2} (θ) (1 - cos^{2} (θ)) = cos^{2} (θ)

sin (\frac{π}{3} + x) - cos (\frac{π}{6} + x) = sin (x)

Is cos(4θ)=8cos^4(θ)-8cos^2(θ)+1 ?
The answer to whether cos(4θ)=8cos^4(θ)-8cos^2(θ)+1 is True