Is (cos(θ))/(1-sin^2(θ))= 1/(cos(θ)) ?

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

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prove (cos(θ))/(1-sin^2(θ))= 1/(cos(θ))

prove

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

True

Solution steps

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

Manipulating left side

\frac{cos ( θ )}{1 - sin ^{2} ( θ )}

Rewrite using trig identities

\frac{cos ( θ )}{1 - sin ^{2} ( θ )}

Use the Pythagorean identity:

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

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

= \frac{cos ( θ )}{cos ^{2} ( θ )}

Cancel the common factor:

cos (θ)

= \frac{1}{cos ( θ )}

= \frac{1}{cos ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

\frac{1 - tan ^{4} ( θ )}{sec ^{2} ( θ )} = 1 - tan^{2} (θ)

(1 + csc (θ)) (1 - sin (θ)) = csc (θ) - sin (θ)

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

sin^{2} (x) cos^{2} (x) = \frac{1}{8} (1 - sin (4 x))

\frac{1 - tan ( x )}{1 - cot ( x )} = - tan (x)

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