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

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

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

prove

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

False

Solution steps

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

Show that the two sides are not equal

For

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

plug in

x = 1

\frac{1 - cos ^{2} ( 1 )}{1 + sin ( 1 )} = 0.38451 \dots

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

Refine to a decimal form

= 0.38451 \dots

sin (1) = 0.84147 \dots

sin (1)

Refine to a decimal form

= 0.84147 \dots

The two sides are not equal

\Rightarrow False

cos (θ) \cdot tan (θ) \cdot csc (θ) = 1

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

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

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

\frac{- cot ( x ) + 1}{tan ( x ) - 1} = cot (x)

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