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

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

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

prove

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

True

Solution steps

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

Manipulating left side

tan (2 x) (1 - tan^{2} (x))

Rewrite using trig identities

tan (2 x) (1 - tan^{2} (x))

Use the Double Angle identity:

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

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

Simplify

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

Cancel the common factor:

1 - tan^{2} (x)

= 2 tan (x)

= 2 tan (x)

= 2 tan (x)

We showed that the two sides could take the same form

\Rightarrow True

csc (x) - cos (x) \cdot cot (x) = sin (x)

sin (x) \cdot csc (x) = 1

csc^{2} (θ) (1 - cos^{2} (θ)) = sin (648 0^{\circ})

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

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

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