Question

prove that √1+cos A/√1- cos A =1/cosec A - cot A​

Answer 1

Step-by-step explanation:

$\sqrt{1+ cos A}$ /$\sqrt{1 - cos A}$

Multiply both the numerator and the denominator by $\sqrt{1 - cos A}$

=$\sqrt{(1 + cos A)(1 - cos A)}$ / (1 - cos A)

=$\sqrt{( 1 - cos^{2}A) }$ / (1 - cos A)

=$\sqrt{sin^{2}A }$ / (1 - cos A)

= sinA / (1 - cos A)

Divide the numerator and the denominator by sin A , we get

1/( $\frac{1}{sin A}$ - $\frac{cosA}{sinA}$ )

= $\frac{1}{( cosec A - cot A)}$