Is sin(θ)(csc(θ)-sin(θ))=cos^2(θ) ?

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

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prove sin(θ)(csc(θ)-sin(θ))=cos^2(θ)

prove

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

True

Solution steps

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

Manipulating left side

sin (θ) (csc (θ) - sin (θ))

Express with sin, cos

= 1 - sin^{2} (θ)

Rewrite using trig identities

= cos^{2} (θ)

We showed that the two sides could take the same form

\Rightarrow True

sec (y) cos (y) = 1

csc (x) - sin (x) = cos (x) \cdot cot (x)

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

\frac{sec ^{2} ( θ )}{tan ( θ )} = sec (θ) csc (θ)

sec (2 x) = \frac{1 + tan ^{2} ( x )}{1 - tan ^{2} ( x )}

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