Is (1-cos(θ))(1+sec(θ))=sec(θ)-cos(θ) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

(1 - cos (θ)) (1 + sec (θ))

Express with sin, cos

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

Expand

(1 + cos (θ)) (1 - cos (θ)) : 1 - cos^{2} (θ)

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

Manipulating right side

sec (θ) - cos (θ)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

tan (x) csc (x) sec (x) = tan^{2} (x) + 1

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

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

tan^{2} (x) csc^{2} (x) cot^{2} (x) sin^{2} (x) = 1

sec (x) cot (x) sin (x) = 1

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