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

The answer to whether (1-2sin^2(x))/(1-sin^2(x))=1-tan(2x) is False

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

\frac{1 - 2 sin ^{2} ( 1 )}{1 - sin ^{2} ( 1 )} = - 1.42551 \dots

\frac{1 - 2 sin ^{2} ( 1 )}{1 - sin ^{2} ( 1 )}

Refine to a decimal form

= - 1.42551 \dots

1 - tan (2 \cdot 1) = 3.18503 \dots

1 - tan (2 \cdot 1)

Refine to a decimal form

= 3.18503 \dots

The two sides are not equal

\Rightarrow False

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