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

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

\frac{csc ^{2} ( x )}{cot ( x )} = csc (x) \cdot sec (x)

(1 - sin (x)) + (1 + sin (x)) = 2 cos (x)

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

tan^{2} (θ) + 4 = sec^{2} (θ) + 3

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