Is csc(θ)cos^2(θ)+sin(θ)=csc(θ) ?

The answer to whether csc(θ)cos^2(θ)+sin(θ)=csc(θ) is True

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prove csc(θ)cos^2(θ)+sin(θ)=csc(θ)

prove

csc (θ) cos^{2} (θ) + sin (θ) = csc (θ)

True

Solution steps

csc (θ) cos^{2} (θ) + sin (θ) = csc (θ)

Manipulating left side

csc (θ) cos^{2} (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

sec (θ + \frac{π}{2}) = csc (θ)

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

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

cos (A) csc (A) = cot (A)

tan (θ) = \frac{1 - cos ( 2 θ )}{sin ( 2 θ )}

Is csc(θ)cos^2(θ)+sin(θ)=csc(θ) ?
The answer to whether csc(θ)cos^2(θ)+sin(θ)=csc(θ) is True