Question

prove the identity sin^2x + tan^2xsin^2x = tan^2x

Answer 1

Double angle formula

Answer 2

sin^2(x) (1+tan^2(x)) = sin^2(x)*sec^2(x) = tan^2(x)

Answer 3

nice, that's an easier way to do it ^

you could also do it this way:

tan^2x - sin^2x= tan^2xsin^2x
sin^2x/cos^2x - sin^2x= tan^2xsin^2x
sin^2x ( 1/cos^2x - 1) = tan^2xsin^2x
sin^2x ( 1-cos^2x/ cos^2x) = tan^2xsin^2x
sin^2 x (sin^2x / cos^2x) = tan^2xsin^2x
sin^2xtan^2x = tan^2xsin^2x

Answer 4

thanks but any without sec

Answer 5

sec x = 1/cos x
Therefore, sec^2x = 1/cos^2x
and sin^2x/cos^2x = tan^2x since tan x = sin x/cos x

I'm not sure if this answers your question for an answer without sec

Answer 6

thanks guys