Question

How do I get cos(2x)-1=-2sin^2 x ?

Answer 1

look at the attachment.

Answer 2

wow thanks. Why is it that \[\cos 2x=\cos x \cos x-\sin x \sin x\] ?

Answer 3

it is a general rule. cos(a+b)=cosacosb-sinasinb. if you write cos2x as cos(x+x) you can expand as to that rule.

Answer 4

I dont know what this rule is called in your terminology. but it is calles as "half angle formula". \[\sin(a+b)=\sin(a) \cos(b)+\sin(b) \cos(a)
and for cosinus \cos(a+b)=\cos(a)\cos(b)-\sin(a)\sin(b)\]

Answer 5

..and if \[\cos ^{2}x=1-\sin^2x\] then \[\sin ^2x=1+\cos^2x\]
right?

Answer 6

nope \[\sin ^{2}x=1-\cos ^{2}x\]

Answer 7

ok thanks a bunch

Answer 8

your welcome :)