Is (sqrt(1-sin(a)))/(1+sin(a))=(cos(a))/(1+sin(a)) ?

The answer to whether (sqrt(1-sin(a)))/(1+sin(a))=(cos(a))/(1+sin(a)) is False

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prove (sqrt(1-sin(a)))/(1+sin(a))=(cos(a))/(1+sin(a))

prove

\frac{1 - sin ( a )}{1 + sin ( a )} = \frac{cos ( a )}{1 + sin ( a )}

False

Solution steps

\frac{1 - sin ( a )}{1 + sin ( a )} = \frac{cos ( a )}{1 + sin ( a )}

Show that the two sides are not equal

For

\frac{1 - sin ( a )}{1 + sin ( a )} = \frac{cos ( a )}{1 + sin ( a )}

plug in

a = 1

\frac{1 - sin ( 1 )}{1 + sin ( 1 )} = 0.21621 \dots

\frac{1 - sin ( 1 )}{1 + sin ( 1 )}

Refine to a decimal form

= 0.21621 \dots

\frac{cos ( 1 )}{1 + sin ( 1 )} = 0.29340 \dots

\frac{cos ( 1 )}{1 + sin ( 1 )}

Refine to a decimal form

= 0.29340 \dots

The two sides are not equal

\Rightarrow False

2 \cdot cos (x) \cdot sin (x) = sin (2 x)

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

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

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

tan (θ) cos (θ) - sin^{2} (θ) = cos^{2} (θ)

Is (sqrt(1-sin(a)))/(1+sin(a))=(cos(a))/(1+sin(a)) ?
The answer to whether (sqrt(1-sin(a)))/(1+sin(a))=(cos(a))/(1+sin(a)) is False