Is 1-2sin^2(2θ)=8cos^4(θ)-8cos^2(θ)+1 ?

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

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prove 1-2sin^2(2θ)=8cos^4(θ)-8cos^2(θ)+1

prove

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

True

Solution steps

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

Manipulating left side

1 - 2 sin^{2} (2 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

sech^{2} (x) + tanh^{2} (x) = 1

sec (x) cos (x) - 2 cos^{2} (x) = - (cos (2 x))

2 cos^{2} (A) - cos (2 A) - 1 = 0

\frac{( 2 sec ( x ) )}{tan ( x )} = 2 csc (x)

\frac{cot ( x ) + 1}{cos ( x ) + sin ( x )} = csc (x)

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