Question

Prove the identity.

2cos^2 x/1-cos^2 x = 2/tan^2 x

Answer 1

do you recall a trigonometric identity relating
sin^2 x and cos^2 x
?

Answer 2

yes i do, i tried to sub in what fits to the identities but I'm still messing up

Answer 3

ok,

so we have
\(\Large \sin^2 x+\cos^2 x=1\)
try to isolate sin^2 x ?

Answer 4

subtract cos^2 x from both sides, what u get ?

Answer 5

so like this?

sin^2x - cos^2 x = 1-cos^2 x

Answer 6

\(\Large \sin^2 x+\cos^2 x=1\)
\(\Large \sin^2 x+\cos^2 x-\cos^2 x=1-\cos^2 x \)
\(\Large \sin^2 x = 1-\cos^2 x\)
got this ?

Answer 7

oh yeah i forgot the first cos^2 but yup i get it :)

Answer 8

so your denominator is just sin^2 x, right ?

Answer 9

yup :)
and now from there i have to make it equal to the 2/tan^2 x?

Answer 10

correct

Answer 11

well that was easy, thank you! :)

Answer 12

welcome :)