Question

prove cosec theta/cosec theta -1+cosec theta/cosec theta+1=2sec^2theta

PLEASE SHOW WHOLE PROCESS

IN GOOD HAND WRITING

Answer 1

Hi ,

Here I used A instead of theta.

LHS= CosecA/(cosecA-1)+cosecA/(cosecA+1 )

= CosecA [1/(cosecA-1) +1/(Cosec A+1)]

= CosecA[(cosecA+1+cosec A -1)/(cosecA-1 )(cosec A+1 )]

= ( 2cosec²A ) / [ cosec² A - 1 ]

= 2cosec²A / cot² A

= 2 ( 1/sin² A ) / ( cos² A/sin² A )

= 2/cos² A

= 2sec²A

= RHS

Answer 2

hope it helps u ........in ending I skipped some steps hope will able to find it out