Is cos(θ)cot(θ)+sin(θ)=csc(θ) ?

The answer to whether cos(θ)cot(θ)+sin(θ)=csc(θ) is True

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prove cos(θ)cot(θ)+sin(θ)=csc(θ)

prove

cos (θ) cot (θ) + sin (θ) = csc (θ)

True

Solution steps

cos (θ) cot (θ) + sin (θ) = csc (θ)

Manipulating left side

cos (θ) cot (θ) + sin (θ)

Express with sin, cos

= \frac{cos ^{2} ( θ ) + sin ^{2} ( θ )}{sin ( θ )}

Rewrite using trig identities

= \frac{1}{sin ( θ )}

Rewrite using trig identities

csc (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

(csc (θ) + 1) (csc (θ) - 1) = cot^{2} (θ)

cos (θ) (cot (θ) + tan (θ)) = csc (θ)

sin (- θ) = - sin (θ)

- sin (x) = sin (- x)

Is cos(θ)cot(θ)+sin(θ)=csc(θ) ?
The answer to whether cos(θ)cot(θ)+sin(θ)=csc(θ) is True