Is (tan(θ))/(1+sec(θ))=-cot(θ)+csc(θ) ?

The answer to whether (tan(θ))/(1+sec(θ))=-cot(θ)+csc(θ) is True

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prove (tan(θ))/(1+sec(θ))=-cot(θ)+csc(θ)

prove

\frac{tan ( θ )}{1 + sec ( θ )} = - cot (θ) + csc (θ)

True

Solution steps

\frac{tan ( θ )}{1 + sec ( θ )} = - cot (θ) + csc (θ)

Manipulating left side

\frac{tan ( θ )}{1 + sec ( θ )}

Express with sin, cos

= \frac{sin ( θ )}{1 + cos ( θ )}

Manipulating right side

- cot (θ) + csc (θ)

Express with sin, cos

= \frac{1 - cos ( θ )}{sin ( θ )}

Rewrite using trig identities

= \frac{sin ( θ )}{1 + cos ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

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

cos (2 x - 90) = 2 sin (x) cos (x)

sin^{4} (x) - 2 sin^{2} (x) = cos^{4} (x) - 1

cot^{4} (a) = \frac{cos ^{4} ( a )}{sin ^{4} ( a )}

1 + sec^{2} (x) sin (x) = sec^{2} (x)

Is (tan(θ))/(1+sec(θ))=-cot(θ)+csc(θ) ?
The answer to whether (tan(θ))/(1+sec(θ))=-cot(θ)+csc(θ) is True