Question

What is the simplified value of (cosec A + sin A) (cosec A – sin A)? ​

Answer 1

LHS = ( cosecA + sinA )(cosecA-SinA)

= Cosec² A - sin² A........(i)

As we know that,

1 ) cosec² A = 1 + cot² A .....(ii)

2 ) sin² A = 1 - cos² A.......(iii)

Now putting the value of (ii) and (iii) in (i),

= 1 + cot² A - ( 1 - cos² A )

= 1 + cot² A - 1 + cos² A

= cot² A + cos² A

= RHS

Hence,proved.

Hope it helps.