Is tan(θ)(csc(θ)-sin(θ))=cos(θ) ?

The answer to whether tan(θ)(csc(θ)-sin(θ))=cos(θ) is True

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prove tan(θ)(csc(θ)-sin(θ))=cos(θ)

prove

tan (θ) (csc (θ) - sin (θ)) = cos (θ)

True

Solution steps

tan (θ) (csc (θ) - sin (θ)) = cos (θ)

Manipulating left side

tan (θ) (csc (θ) - sin (θ))

Express with sin, cos

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

Rewrite using trig identities

= cos (θ)

We showed that the two sides could take the same form

\Rightarrow True

cot^{2} (x) sec^{2} (x) = csc^{2} (x)

sin (10 θ) = 2 sin (5 θ) cos (5 θ)

\frac{cos ( θ ) sec ( θ )}{tan ( θ )} = cot (θ)

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

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

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