Question

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

Answer 1

$\huge \bf \color{green} \mathfrak{Question : - }$

Prove that ;

1+cosA/sinA = sinA/1-cosA

$\huge \bf \color{orange} \mathfrak{Proof : - }$

$\frac{1 + cosA}{sinA} = \frac{sinA}{1 - cosA} \\ \\ \frac{1 + cosA}{sinA} = \frac{sinA}{1 - cosA} \\ \\ \frac{1 + cosA}{sinA} = \frac{sinA}{1 - cosA} \times \frac{1 + cosA}{1 + cosA} \\ \\ \frac{1 + cosA}{sinA} = \frac{sinA(1 + cosA)}{1 - {cos}^{2}A } \\ \\ \frac{1 + cosA }{sinA} = \frac{sinA(1 + cosA)}{ {sin}^{2} A} \\ \\ \frac{1 + cosA}{sinA} = \frac{1 + cosA}{sinA} \\ \\ L.H.S. = R.H.S.$