Is csc(θ)sec(θ)-cot(θ)=tan(θ) ?

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

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prove csc(θ)sec(θ)-cot(θ)=tan(θ)

prove

csc (θ) sec (θ) - cot (θ) = tan (θ)

True

Solution steps

csc (θ) sec (θ) - cot (θ) = tan (θ)

Manipulating left side

csc (θ) sec (θ) - cot (θ)

Express with sin, cos

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

Rewrite using trig identities

= \frac{sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

= tan (θ)

We showed that the two sides could take the same form

\Rightarrow True

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

\frac{sin ( x ) - csc ( x )}{csc ( x )} = - cos^{2} (x)

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

tan (2 x) - 2 tan (2 x) sin^{2} (x) = sin (2 x)

cot^{2} (θ) csc^{2} (θ) - cot^{2} (θ) = cot^{4} (θ)

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