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

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

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prove 1-(cos^2(x))/(1+sin^2(x))=sin(x)

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

1 - \frac{cos ^{2} ( 1 )}{1 + sin ^{2} ( 1 )} = 0.82909 \dots

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

Refine to a decimal form

= 0.82909 \dots

sin (1) = 0.84147 \dots

sin (1)

Refine to a decimal form

= 0.84147 \dots

The two sides are not equal

\Rightarrow False

\frac{1}{2} sec (x) - 1 = 0

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

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

\frac{cos ( x )}{1 + sin ( x )} + tan (x) = cos (x)

cot^{2} (x) sec^{2} (x) = 1 + \frac{1}{tan ^{2} ( x )}

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