Is (tan(θ))/(csc(θ))=sec(θ)-cos(θ) ?

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

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prove (tan(θ))/(csc(θ))=sec(θ)-cos(θ)

prove

\frac{tan ( θ )}{csc ( θ )} = sec (θ) - cos (θ)

True

Solution steps

\frac{tan ( θ )}{csc ( θ )} = sec (θ) - cos (θ)

Manipulating left side

\frac{tan ( θ )}{csc ( θ )}

Express with sin, cos

= \frac{sin ^{2} ( θ )}{cos ( θ )}

Rewrite using trig identities

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

Manipulating right side

sec (θ) - cos (θ)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

cot (2 β) = \frac{cot ^{2} ( β ) - 1}{2 cot ( β )}

csc^{2} (y) tan^{2} (y) - 1 = tan^{2} (y)

cot (θ) tan (θ) = 1

4 cos^{2} (x) - 2 = - 1

cot (2 x) = \frac{1}{2} (cot (x) - tan (x))

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