Is tan(2a)-tan(a)=tan(a)sec(2a) ?

The answer to whether tan(2a)-tan(a)=tan(a)sec(2a) is True

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prove tan(2a)-tan(a)=tan(a)sec(2a)

prove

tan (2 a) - tan (a) = tan (a) sec (2 a)

True

Solution steps

tan (2 a) - tan (a) = tan (a) sec (2 a)

Manipulating left side

tan (2 a) - tan (a)

Express with sin, cos

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

Rewrite as

= sin (2 a) cos (a) - cos (2 a) sin (a)

Rewrite using trig identities

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

Manipulating right side

tan (a) sec (2 a)

Express with sin, cos

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

We showed that the two sides could take the same form

\Rightarrow True

sin^{2} (x) - 4 cos^{2} (x) = 5 sin^{2} (x) - 4

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

\frac{1 + tan ^{2} ( u )}{1 - tan ^{2} ( u )} = \frac{1}{cos ^{2} ( u ) - sin ^{2} ( u )}

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

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

Is tan(2a)-tan(a)=tan(a)sec(2a) ?
The answer to whether tan(2a)-tan(a)=tan(a)sec(2a) is True