Is cos^2(B)-sin^2(B)=2cos^2(B)-1 ?

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

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prove cos^2(B)-sin^2(B)=2cos^2(B)-1

prove

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

True

Solution steps

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

Manipulating left side

cos^{2} (B) - sin^{2} (B)

Rewrite using trig identities

= 2 cos^{2} (B) - 1

We showed that the two sides could take the same form

\Rightarrow True

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

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

cot (t) tan (t) = 1

1 + tan^{2} (t) = sec^{2} (t)

sec^{2} (x) = \frac{csc ( x )}{csc ( x ) - sin ( x )}

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