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

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

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prove csc(2x)=(1+tan^2(x))/(2tan(x))

prove

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

True

Solution steps

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

Manipulating right side

\frac{1 + tan ^{2} ( x )}{2 tan ( x )}

Express with sin, cos

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

Rewrite using trig identities

= \frac{1}{sin ( 2 x )}

Rewrite using trig identities

csc (2 x)

We showed that the two sides could take the same form

\Rightarrow True

sin (θ) + cos (θ) = 1

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

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

tan (3 0^{\circ}) = \frac{sin ( 3 0 ^{\circ} )}{cos ( 3 0 ^{\circ} )}

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

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