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

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

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

sin (3 a) + sin (a) = 4 sin (a) - 4 sin^{3} (a)

sin (2 t) = 2 sin (t) (cos (t))

2 sin (x + 4 5^{\circ}) = sin (x) + cos (x)

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