Is (tan(θ)+sec(θ))(1-sin(θ))=cos(θ) ?

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

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

prove

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

True

Solution steps

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

Manipulating left side

(tan (θ) + sec (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

cot (π - x) = - cot (x)

sin (θ) cos (θ) + sin^{3} (θ) sec (θ) = tan (θ)

tan (A) sin (A) = sec (A) - cos (A)

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

sin (x) sec (x) = 1

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