Is (cos(x))/(csc(x)+1)+(cos(x))/(csc(x)-1)=2tan(x) ?

The answer to whether (cos(x))/(csc(x)+1)+(cos(x))/(csc(x)-1)=2tan(x) is True

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prove (cos(x))/(csc(x)+1)+(cos(x))/(csc(x)-1)=2tan(x)

prove

\frac{cos ( x )}{csc ( x ) + 1} + \frac{cos ( x )}{csc ( x ) - 1} = 2 tan (x)

True

Solution steps

\frac{cos ( x )}{csc ( x ) + 1} + \frac{cos ( x )}{csc ( x ) - 1} = 2 tan (x)

Manipulating left side

\frac{cos ( x )}{csc ( x ) + 1} + \frac{cos ( x )}{csc ( x ) - 1}

Express with sin, cos

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

Rewrite using trig identities

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

Rewrite using trig identities

2 tan (x)

We showed that the two sides could take the same form

\Rightarrow True

\frac{cos ( x ) csc ( x )}{cot ^{2} ( x )} = tan (x)

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

cot (\frac{π}{2} - u) = tan (u)

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

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

Is (cos(x))/(csc(x)+1)+(cos(x))/(csc(x)-1)=2tan(x) ?
The answer to whether (cos(x))/(csc(x)+1)+(cos(x))/(csc(x)-1)=2tan(x) is True