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

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

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

prove

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

True

Solution steps

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

Manipulating left side

(tan (x) + sec (x)) (1 - sin (x))

Express with sin, cos

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

Rewrite using trig identities

= cos (x)

We showed that the two sides could take the same form

\Rightarrow True

cos^{2} (B) - sin^{2} (B) = 1 - 2 sin^{2} (B)

cot (x) cos (2 x) = - sin (2 x) + cot (x)

cot (u) tan (u) - cos^{2} (u) = sin^{2} (u)

\frac{csc ^{4} ( x ) - 1}{cot ^{2} ( x )} = csc^{2} (x) + 1

sin (2 x) tan (x) = 1 - cos (2 x)

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