Is cos^2(β)-sin^2(β)=2cos^2(β)-1 ?

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

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prove cos^2(β)-sin^2(β)=2cos^2(β)-1

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (β) - sin^{2} (β)

Rewrite using trig identities

= 2 cos^{2} (β) - 1

We showed that the two sides could take the same form

\Rightarrow True

(1 - cos (β)) (1 + cos (β)) = \frac{1}{csc ^{2} ( β )}

\frac{cot ( θ ) sec ( θ )}{csc ( θ )} = 1

sin (θ) csc (θ) - cos^{2} (θ) = sin^{2} (θ)

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

\frac{1}{1 + tan ^{2} ( x )} = cos^{2} (x)

Is cos^2(β)-sin^2(β)=2cos^2(β)-1 ?
The answer to whether cos^2(β)-sin^2(β)=2cos^2(β)-1 is True