Is (-csc(x))/(sec(x))+(cos(x))/(-sin(x))=-2cot(x) ?

The answer to whether (-csc(x))/(sec(x))+(cos(x))/(-sin(x))=-2cot(x) is True

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prove (-csc(x))/(sec(x))+(cos(x))/(-sin(x))=-2cot(x)

prove

\frac{- csc ( x )}{sec ( x )} + \frac{cos ( x )}{- sin ( x )} = - 2 cot (x)

True

Solution steps

\frac{- csc ( x )}{sec ( x )} + \frac{cos ( x )}{- sin ( x )} = - 2 cot (x)

Manipulating left side

\frac{- csc ( x )}{sec ( x )} + \frac{cos ( x )}{- sin ( x )}

Express with sin, cos

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

Rewrite using trig identities

- 2 cot (x)

We showed that the two sides could take the same form

\Rightarrow True

1 + tan^{2} (\frac{3}{4}) = sec^{2} (x)

2 sin (2 x) + cot (2 x) = csc (2 x) - cos (2 x)

sin (\frac{3 π}{4}) = \frac{1}{2}

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

\frac{5 sin ( 2 θ )}{2 sin ( θ )} = 5 cos (θ)

Is (-csc(x))/(sec(x))+(cos(x))/(-sin(x))=-2cot(x) ?
The answer to whether (-csc(x))/(sec(x))+(cos(x))/(-sin(x))=-2cot(x) is True