Is csc(θ)sec(θ)-csc(θ)cos(θ)=tan(θ) ?

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

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prove csc(θ)sec(θ)-csc(θ)cos(θ)=tan(θ)

prove

csc (θ) sec (θ) - csc (θ) cos (θ) = tan (θ)

True

Solution steps

csc (θ) sec (θ) - csc (θ) cos (θ) = tan (θ)

Manipulating left side

csc (θ) sec (θ) - csc (θ) cos (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

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

cot (x) sec^{2} (x) - cot (x) = tan (x)

\frac{cos ( θ )}{cos ( θ ) - 1} = \frac{1}{1 - sec ( θ )}

cos (- \frac{π}{4} - 5 t) = cos (5 t + \frac{π}{4})

tan (\frac{π}{4} - θ) = \frac{1 - tan ( θ )}{1 + tan ( θ )}

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