Question

1+cosA/1-cosA=(cosecA+cotA)^2

Answer 1

Solution:

LHS = (1+cosA)/(1-cosA)

= [(1+cosA)/(1-cosA)][(1+cosA)/(1+cosA)]

= (1+cosA)²/(1-cos²A)

= (1+cosA)²/sin²A

= [(1+cosA)/sinA]²

= [1/SinA + cosA/sinA]²

= (cosecA + cotA)²

= RHS

••••

Answer 2

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

Left Hand Side

$\bf\huge{\implies\dfrac{1+cosA}{1-cosA}}$        

$\bf\huge{\implies\dfrac{1+cosA}{1-cosA}\times \dfrac{1+cosA}{1+cosA}}$        

 

$\bf\huge{\implies\dfrac{(1+cosA)^2}{1-cos^2 A}}$        

 

$\bf\huge{\implies\dfrac{(1+cosA)^2}{sin^2 A}}$        

$\bf\huge{\implies(\dfrac{(1+cosA)}{sinA})^2}$

$\bf\huge{\implies(\dfrac{1}{sinA} + \dfrac{cosA}{sinA})^2}$

= (cosecA + cotA)²

$\bf\huge\bf\huge{\boxed{\bigstar{{LHS \:= \:RHS}}}}$