I know sin^2(x)+cos^2(x)=1 what does sin^4(x)+cos^4(x)=

Question

anonymous · Answer

anonymous · Answer

but are the two equations similar? can sin^4(x)+cos^4(x)=1? like does (sin^2(x)+cos^2(x))^2=(1)^2 so basically it equals 1?

anonymous · Answer

$$(\large sin^2(x)+\cos^2(x))^2 \neq \sin^4(x)+\cos^4(x)$$

anonymous · Answer

$(a^2+b^2)^2\neq a^4+b^4$ unless one of them is zero

anonymous · Answer

the real question from my homework is $$\sin^{2}x-\cos^{2}x=1-2\cos^{2}x$$
I have to prove that they are equal and only mess with one side

anonymous · Answer

Add both sides by 2cos²(x).

anonymous · Answer

but I can only mess around with one side of the equation to make it equal the other side

anonymous · Answer

Well, we know that sin²x + cos²x = 1 right? So sin² = 1 - cos²x

Replace sin²x to 1 - cos²x in left side of the equation then simplify.

anonymous · Answer

but how does the 2 in the 1-2cos^2 work?

anonymous · Answer

Well, 1 - 2cos²x = 1 - cos²x - cos²x

Not sure exactly what you mean.

anonymous · Answer

which side are you working on?

anonymous · Answer

I'm just going to start a new question but thanks for your help