Is cos(θ)=(sec(θ)+tan(θ))(1-sin(θ)) ?

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

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

prove

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

True

Solution steps

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

Manipulating right 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

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

sec (2 x) = \frac{1}{cos ( 2 x )}

(sin (x) + cos (x)) 2 = 1 + sin (2 x)

cot (x) cos (x) = csc (x) - sin (x)

sec (2 α) 2 - sec (2 α) = sec (2 α)

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