Is (1-sin^2(β))/(cos(β))=cos(β) ?

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

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prove (1-sin^2(β))/(cos(β))=cos(β)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1 - sin ^{2} ( β )}{cos ( β )}

Rewrite using trig identities

\frac{1 - sin ^{2} ( β )}{cos ( β )}

Use the Pythagorean identity:

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

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

= \frac{cos ^{2} ( β )}{cos ( β )}

Cancel the common factor:

cos (β)

= cos (β)

= cos (β)

We showed that the two sides could take the same form

\Rightarrow True

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

csc (2 x) - cot (2 x) = tan (2 x)

sin (x) = 1 - cos (x)

\frac{sec ( 2 x ) + 1}{tan ( 2 x )} = cot (x)

cos^{2} (6 θ) - sin^{2} (6 θ) = cos (12 θ)

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