Question

Cosec²a+sec²a/cosec²a-sec²a=1+tan²a/1-tan²a

Answer 1

$<b>$

we know 

sin x/ cos x = tan x so 1/cos x = tan x/ sin x or sec x= tan x cosec x 

so cosec^2A+ sec^2A = cosec ^2 A + tan ^ 2 A cosec ^2 A = cosec ^2 A( 1+ tan ^2 A) 

and 

cosec^2A - sec^2A = cosec ^2 A - tan ^ 2 A cosec ^2 A = cosec ^2 A( 1- tan ^2 A) 

by deviding we get (cosec^2A+ sec^2A)/ (cosec^2A- sec^2A) = (1+tan^2A)/(1-tan^2A)

Answer 2

we know

sin x/ cos x = tan x so 1/cos x = tan x/ sin x or sec x= tan x cosec x

so cosec^2A+ sec^2A = cosec ^2 A + tan ^ 2 A cosec ^2 A = cosec ^2 A( 1+ tan ^2 A)

and

cosec^2A - sec^2A = cosec ^2 A - tan ^ 2 A cosec ^2 A = cosec ^2 A( 1- tan ^2 A)

by deviding we get (cosec^2A+ sec^2A)/ (cosec^2A- sec^2A) = (1+tan^2A)/(1-tan^2A)