Question

I have to prove this:

(2αsinxcox)^2 +α^2(cos^2 x-sin^2 x)^2= α^2

Answer 1

try using double angle identities to begin with

Answer 2

you should know \[2\sin(x)\cos(x)=\sin(2x) \\ \text{ and } \cos^2(x)-\sin^2(x)=\cos(2x)\]

Answer 3

well you a few trig identities

2sin(A)cos(A) = sin(2A)

cos^2(A) - sin^2(A) = cos(2A)

so you get

\[(\alpha \sin(2x))^2 + \alpha^2(\cos(2x))^2 = \alpha^2\]

so if you simplify this you get

\[\alpha^2\sin^2(2x) + \alpha^2\cos^2(2x) = \alpha^2\]

now factor the left hand side and you should see a well known trig identity

hope it helps

Answer 4

\[\sin ^{2}(2x) + \cos ^{2}(2x)= 1 \]

just like \[\sin ^{2}x+ \cos ^{2}x=1\] does, right?

Answer 5

that's correct