Question

if tan=1/ROOT7 then show that cosec^2tita-sec^2tita/cosec^2tita+sec^2tita=3/4

Answer 1

tan© =1/√7

tan^2© = 1/7

we know,

sec^2© -tan^2© = 1

sec^2© = 1 + tan^2©
=1 + 1/7 = 8/7

also know ,

tan© = 1/cot©

cot© = √7

cot^2 =7

use formula ,
cosec^2© -cot^2© = 1

hence,

cosec^2 ©= 1+7 =8

now,

LHS =(cosec^2© - sec^2©)/(cosec^2© +sec^2©)

=( 8 - 8/7 )/( 8 + 8/7)

=(56 -8)/(56 + 8)

=48/64

=3/4 = RHS