Is (sec(θ)+tan(θ))(1-sin(θ))=cos(θ) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

(sec (θ) + tan (θ)) (1 - sin (θ))

Express with sin, cos

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

Rewrite using trig identities

= cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

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sin (arcsin (x) + arccos (x)) = 1

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

(sec (5 x) - 1) (sec (5 x) - 1) = tan^{2} (5 x)

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

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