Is csc^2(x)tan(x)-cot(x)=tan(x) ?

The answer to whether csc^2(x)tan(x)-cot(x)=tan(x) is True

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prove csc^2(x)tan(x)-cot(x)=tan(x)

prove

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

True

Solution steps

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

Manipulating left side

csc^{2} (x) tan (x) - cot (x)

Express with sin, cos

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

Rewrite using trig identities

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

Use the basic trigonometric identity:

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

= tan (x)

We showed that the two sides could take the same form

\Rightarrow True

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

tan^{- 3} (x) = (tan (x))^{- 3}

\frac{1}{- 6 csc ^{2} ( 6 x - 1 )} = - \frac{sin ^{2} ( 6 x - 1 )}{6}

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

csc (2 x) = \frac{- 2 3}{3}

Is csc^2(x)tan(x)-cot(x)=tan(x) ?
The answer to whether csc^2(x)tan(x)-cot(x)=tan(x) is True