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

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

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

prove

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

True

Solution steps

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

Manipulating left side

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

Rewrite using trig identities

= 1 - 2 sin^{2} (b)

We showed that the two sides could take the same form

\Rightarrow True

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

(csc (x) - 1) (csc (x) + 1) = cot^{2} (x)

tan^{2} (y) (csc^{2} (y) - 1) = 1

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

1 - cos (θ) = sin (θ)

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