Is cos(2θ)=1-2sin^2(θ) ?

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

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prove cos(2θ)=1-2sin^2(θ)

prove

cos (2 θ) = 1 - 2 sin^{2} (θ)

True

Solution steps

cos (2 θ) = 1 - 2 sin^{2} (θ)

Manipulating left side

cos (2 θ)

Rewrite using trig identities

= cos^{2} (θ) - sin^{2} (θ)

Use the Pythagorean identity:

cos^{2} (θ) + sin^{2} (θ) = 1

cos^{2} (θ) = 1 - sin^{2} (θ)

= 1 - sin^{2} (θ) - sin^{2} (θ)

Simplify

1 - sin^{2} (θ) - sin^{2} (θ) : 1 - 2 sin^{2} (θ)

= 1 - 2 sin^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

sin (x) = 1 - cos (x)

\frac{cos ( θ )}{cot ( θ )} = sin (θ)

sin (θ) = \frac{tan ( θ )}{sec ( θ )}

\frac{sec ( y )}{tan ( y ) + cot ( y )} = sin (y)

\frac{sin ^{2} ( θ )}{( 1 - cos ( θ ) )} = 1 + cos (θ)