Is tan(2x)-tan(x)=(tan(x))/(cos(2x)) ?

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

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prove tan(2x)-tan(x)=(tan(x))/(cos(2x))

prove

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

True

Solution steps

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

Manipulating left side

tan (2 x) - tan (x)

Express with sin, cos

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

Rewrite as

= sin (2 x) cos (x) - cos (2 x) sin (x)

Rewrite using trig identities

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

Manipulating right side

\frac{tan ( x )}{cos ( 2 x )}

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

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

4 sec^{2} (θ) - 3 = 1 + 4 tan^{2} (θ)

sec (θ) = csc (θ) tan (θ)

- sin (x) = sin (x)

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

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