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

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

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

prove

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

True

Solution steps

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

Manipulating left side

2 csc (2 x)

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{sin ( x ) cos ( x )}

Manipulating right side

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

Express with sin, cos

= \frac{1}{cos ( x ) sin ( x )}

We showed that the two sides could take the same form

\Rightarrow True

\frac{sec ^{2} ( t )}{tan ( t )} = cot (t) + tan (t)

csc (\frac{π}{2} - x) = sec (x)

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

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

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

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