Question

1-sinA+cosA / sinA+cosA-1 = 1+cosA/sinA​

Answer 1

Solution:

$\dfrac{\left[\left(\sin ^{2} A+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]\right.}{\left[\left(1-\cos ^{2} A\right)-(1-\cos A)^{2}\right]}$

$\dfrac{\left[\left(1-\cos ^{2} A\right)+2 \times \sin A \times (1-\cos A)+(1-\cos A)^{2}\right]}{\left[(1-\cos A)(1+\cos A)-(1-\cos A)^{2}\right]}$

$\dfrac{(1-\cos A)[1+\cos A+2 \sin A+1-\cos A]}{[1-\cos A][1+\cos A-1+\cos A]}$

$\dfrac{[2+2 \sin A]}{[2 \times \cos A]}$

$\dfrac{2(1+\sin A)}{2 \times \cos A}$

$\dfrac{1+\cos A}{\sin A}$

Hence Proved.