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

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

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

prove

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

True

Solution steps

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

Manipulating left side

(1 - cos (x)) (1 + sec (x))

Express with sin, cos

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

Expand

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

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

Manipulating right side

sec (x) - cos (x)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

6 sin (5 π - x) = 6 sin (x)

2 sin (θ) cos (θ) = sin (2 θ)

tan^{4} (x) + tan^{2} (x) + 1 = sec^{4} (x)

tan^{3} (x) - cot^{3} (x) = tan^{2} (x) sin^{2} (x)

csc^{2} (θ) = cot^{2} (θ) + 1

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