Question

Prove that Tan x/secx-1+tanx/secx+1=2cosecx

Answer 1

sinx/cosx / 1/cosx -1 + sinx/ cosx / 1/cosx+1

sinx/cosx / 1-cosx /cosx + sinx/cosx /1+cosx/cosx

sinx/1-cosx + sinx/1+cosx

sinx(1+cosx) + sinx(1-cosx) / (1-cosx) (1+cosx)

sinx +sinx cosx +sinx -sinx cosx / (1-cosx) (1+cosx)

2sinx / ( 1-cos^2x)

2sinx / sin^2x

2/ sinx

2cosecx