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

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

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prove (1+sec(θ))/(tan(θ)+sin(θ))=csc(θ)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1 + sec ( θ )}{tan ( θ ) + sin ( θ )}

Express with sin, cos

= \frac{1}{sin ( θ )}

Rewrite using trig identities

csc (θ)

We showed that the two sides could take the same form

\Rightarrow True

\frac{1}{sec ( x )} = cos (x)

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

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

- tan (θ) cos (θ) = sin (- θ)

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

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