Question

how does cos2x come out to 1-2sin^2x?

Answer 1

Well...

Answer 2

cos(a+b)=cos a cos b-sin a sin b

Answer 3

cos(theta+theta)= cos theta cos theta - sin theta sin theta

Answer 4

thus cos(2theta)=cos^2 theta - sin^2 theta

Answer 5

we know that sin^2 theta+ cos^2 theta=1 for all real values of theta

Answer 6

so we can safely substitute cos^2 theta=1- sin^2 theta

Answer 7

wowww thank you soo much! haha that makes a lot of sense! :)

Answer 8

kay :)
Just a tip here, whenever you see sin^2 or cos^2 x always see if you can simplify it using substitution. Never forget that sin^2 x+cos^2 x=1!

Answer 9

ok!