Is cos(θ)(csc(θ)-sec(θ))=cot(θ)-1 ?

The answer to whether cos(θ)(csc(θ)-sec(θ))=cot(θ)-1 is True

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prove cos(θ)(csc(θ)-sec(θ))=cot(θ)-1

prove

cos (θ) (csc (θ) - sec (θ)) = cot (θ) - 1

True

Solution steps

cos (θ) (csc (θ) - sec (θ)) = cot (θ) - 1

Manipulating left side

cos (θ) (csc (θ) - sec (θ))

Express with sin, cos

= \frac{cos ( θ ) - sin ( θ )}{sin ( θ )}

Manipulating right side

cot (θ) - 1

Express with sin, cos

= \frac{cos ( θ ) - sin ( θ )}{sin ( θ )}

We showed that the two sides could take the same form

\Rightarrow True

tan^{4} (x) - sec^{4} (x) = 1 - 2 sec^{2} (x)

csc (x) + 1 = \frac{cot ( x )}{sec ( x ) - tan ( x )}

sin (x) sec^{2} (x) = \frac{tan ( x )}{cos ( x )}

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

sin (2 θ) = 2 cot (θ) sin^{2} (θ)

Is cos(θ)(csc(θ)-sec(θ))=cot(θ)-1 ?
The answer to whether cos(θ)(csc(θ)-sec(θ))=cot(θ)-1 is True