Is 1/(sin(θ)cos(θ))-1/(tan(θ))=tan(θ) ?

The answer to whether 1/(sin(θ)cos(θ))-1/(tan(θ))=tan(θ) is True

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prove 1/(sin(θ)cos(θ))-1/(tan(θ))=tan(θ)

prove

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

True

Solution steps

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

Manipulating left side

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

6 sin (\frac{π}{6}) = 2 + 2 sin (\frac{π}{6})

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

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

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

- tan (y) + sec (y) = \frac{cos ( y )}{1 + sin ( y )}

Is 1/(sin(θ)cos(θ))-1/(tan(θ))=tan(θ) ?
The answer to whether 1/(sin(θ)cos(θ))-1/(tan(θ))=tan(θ) is True