Question

1-cosA/1+cosA=(Coseco-cot)²​

Answer 1

Refer attachment

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Answer 2

Corrected Question :

• ${\sf{\dfrac{1 - cosA}{1 + cosA} = \[Coseco - cot\]^2}}$

A N S W E R :

• ${\sf{\bigg[cosecA - cotA\bigg]^2}}$

S O L U T I O N :

• ${\sf{\dfrac{1 - cosA}{1 + cosA} × \dfrac{1 - cosA}{1 + cosA}}}$

${\sf{\dfrac{\bigg(1 - cosA\bigg)^2}{1 - cos^2A}}}$$~~~~~~~~$$\boxed{\sf\purple{[∵ 1 - cos^2Ø = sinØ]}}$

:$\implies$${\sf{\dfrac{\bigg(1 - cosA\bigg)^2}{sin^2A}}}$

$~~~~~$:$\implies$${\sf{\bigg[\dfrac{1 - cosA}{sinA}\bigg]^2}}$

$~~~~~~~~~~$:$\implies$${\sf{\bigg[\dfrac{1}{sinA} - \dfrac{cosA}{sinA}\bigg]^2}}$

$~~~~~~~~~~~~~~~$:$\implies$${\underline{\boxed{\frak{\pink{\bigg[cosecA - cotA\bigg]^2}}}}}$★

Hence,

• R.H.S = L.H.S

$~~~~$$\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Proved!}}}}$

$~~~~~~~~~~~~~~~$ ____________________