What is (sin(θ))/(1+sin(θ))-(sin(θ))/(1-sin(θ)) ?

The solution to (sin(θ))/(1+sin(θ))-(sin(θ))/(1-sin(θ)) is -2tan^2(θ)

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simplify (sin(θ))/(1+sin(θ))-(sin(θ))/(1-sin(θ))

simplify

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

- 2 tan^{2} (θ)

Solution steps

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

Join

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

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

Simplify

(sin (θ) + 1) (- sin (θ) + 1) : cos^{2} (θ)

= - \frac{2 sin ^{2} ( θ )}{cos ^{2} ( θ )}

Simplify

\frac{2 sin ^{2} ( θ )}{cos ^{2} ( θ )} : 2 tan^{2} (θ)

= - 2 tan^{2} (θ)

8 a - 4 b + 16 c + 12 d

((- \frac{1}{2}) y^{4})^{3} \cdot (- 16 y^{2})

sin (x) tan (x) + cos (x)

\frac{y ^{9}}{y ^{3}}

3 + 22 - 3 - 22

What is (sin(θ))/(1+sin(θ))-(sin(θ))/(1-sin(θ)) ?
The solution to (sin(θ))/(1+sin(θ))-(sin(θ))/(1-sin(θ)) is -2tan^2(θ)