Is (tan(β)+sec(β))(1-sin(β))=cos(β) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

(tan (β) + sec (β)) (1 - sin (β))

Express with sin, cos

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

Rewrite using trig identities

= cos (β)

We showed that the two sides could take the same form

\Rightarrow True

sin (α + β) = sin (α) cos (β) + sin (β) cos (α)

sin (x) = \frac{tan ( x )}{sec ( x )}

2 - sec^{2} (z) = 1 - tan^{2} (z)

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

\frac{1}{1 - tan ^{2} ( θ )} + \frac{1}{1 - cot ^{2} ( θ )} = 1

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