Verify the identitiy tan x1cos2 x csc x sec x1sin xSolutio

Verify the identitiy: (tan x/1-cos^2 x) + csc x = (sec x+1)/sin x

Solution

(tan x/1-cos² x) + csc x

since sin²x+cos²x=1 =>1-cos²x=sin²x

=(tan x/sin²x) + csc x

write tanx as sinx /cosx , cscx as 1/sinx

=((sinx/cosx)/sin²x) + (1/sinx)

=((1/cosx)/sinx) + (1/sinx)

write 1/cosx as secx

=(secx /sinx) + (1/sinx)

=(secx+1)/sinx

hence (tan x/1-cos² x) + csc x=(secx+1)/sinx