Is (1-cos(2a))/(1+cos(2a))=tan^2(a) ?

The answer to whether (1-cos(2a))/(1+cos(2a))=tan^2(a) is True

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prove (1-cos(2a))/(1+cos(2a))=tan^2(a)

prove

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

True

Solution steps

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

Manipulating left side

\frac{1 - cos ( 2 a )}{1 + cos ( 2 a )}

Rewrite using trig identities

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

Rewrite using trig identities

tan^{2} (a)

We showed that the two sides could take the same form

\Rightarrow True

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

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

csc (x) tan (x) cos^{2} (x) = cos (x)

sin (a) sin (b) = sin (a + b)

2 sin (x) = \frac{( 4 cos ( x ) - 1 )}{tan ( x )}

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