Is tan(2x)=(2tan(x))/((1-tan^2(x))) ?

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

Popular >

prove tan(2x)=(2tan(x))/((1-tan^2(x)))

prove

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

True

Solution steps

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

Manipulating left side

tan (2 x)

Rewrite using trig identities

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

Simplify

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

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

We showed that the two sides could take the same form

\Rightarrow True

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

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

- csc^{2} (x) = - 1 - (cot (x))^{2}

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

\frac{1}{csc ( θ )} = - cos (θ)

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