Question

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

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Step-by-step explanation:

Solving Left Hand Side

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

Multiply and divide by ( 1 + cosA ) :

$\implies \dfrac{1+cosA}{1-cosA}\times\dfrac{1+cosA}{1+cosA}\\\\\\\implies\dfrac{(1+cosA)^2}{(1-cosA)(1+cosA)}$

From the properties of expansion :

• ( a + b )( a - b ) = a^2 - b^2

$\implies\dfrac{(1+cosA)^2}{1-cos^2A}\\\\\\\implies\dfrac{(1+cosA)^2}{sin^2A}\\\\\\\implies\bigg( \dfrac{1+cosA}{sinA}\bigg)^2\\\\\\\implies\bigg(\dfrac{1}{sinA}+\dfrac{cosA}{sinA}\bigg)^2\\\\\\\implies( cosecA + cotA)^2$

Hence, proved.