Question

Prove the identity. (tanx+1)^2=(1+2sinxcosx)/(cos^2x)
please help!
so far, i have (sin^2x/cos^2x)+(2sinx+1/cosx)
I'm not sure what do next! it seems wrong!

Answer 1

You are virtually there - just add the terms you got to

Answer 2

You have two fractions, one with denominator \(\cos^2(x)\) and one with denominator of \(\cos(x)\). So the common denominator is \(\cos^2(x)\).

Answer 3

(tanx+1)^2 = tan^2x + 2tanx + 1
sin^2x / cos^2x + 2sinx/cosx + 1
= [sin^2x + 2sinxcosx + cos^2x] / cos^2x

sin^x + cos^x = 1

so :

Answer 4

OH i see what i did wrong. THANK YOU SO MUCH :D

Answer 5

your welcome