Question

prove that: 1 - cosA / 1+ cosA=(cotA - cosecA)2​

Answer 1

Answer:-

To find:-

$\frac{1-cosA}{1+cosA}=(cotA-cosecA)^{2}$

Solution:-

$LHS=(cosecA-cotA)^{2}$

$⇒(\frac{1}{sinA}-\frac{cosA}{sinA})$

$⇒(\frac{1-cosA}{sinA}^{2}$

$⇒\frac{(1+cosA)^{2}}{sin^{2}A}$          $[sin^{2}∅+cos^{2}∅=1]$

$⇒\frac{(1-cosA)(1-cosA)}{(1-cosA)(1+cosA)}$

$⇒\frac{(1-cosA)}{(1+cosA)}=RHS$

$\huge\underline\green{Hence \ Proved}$