Is cos(θ)(1/(1-sin(θ)))=sec(θ)+tan(θ) ?

The answer to whether cos(θ)(1/(1-sin(θ)))=sec(θ)+tan(θ) is True

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prove cos(θ)(1/(1-sin(θ)))=sec(θ)+tan(θ)

prove

cos (θ) (\frac{1}{1 - sin ( θ )}) = sec (θ) + tan (θ)

True

Solution steps

cos (θ) \frac{1}{1 - sin ( θ )} = sec (θ) + tan (θ)

Manipulating left side

cos (θ) \frac{1}{1 - sin ( θ )}

Simplify

= \frac{cos ( θ )}{1 - sin ( θ )}

Manipulating right side

sec (θ) + tan (θ)

Express with sin, cos

= \frac{1 + sin ( θ )}{cos ( θ )}

Rewrite using trig identities

= \frac{cos ( θ )}{1 - sin ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

2 sin (a + b) sin (a - b) = cos (2 b) - cos (2 a)

\frac{1}{sin ( x )} = 2

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

(4 sin (θ) + 4 cos (θ)) = 16 + 16 sin (2 θ)

5 sec^{2} (x) = 5 sec^{2} (- x)

Is cos(θ)(1/(1-sin(θ)))=sec(θ)+tan(θ) ?
The answer to whether cos(θ)(1/(1-sin(θ)))=sec(θ)+tan(θ) is True