Question

Trig Identities
Prove:
\[\sin^4x+\cos^4x=\sin^2x(\csc^2x-2\cos^2x)\]

Answer 1

write \(\sin^4x+\cos^4x\) as \((\sin^2x)^2 +(\cos^2x)^2\)
and recall the identity \(a^2+b^2=(a+b)^2-2ab\)

Answer 2

\[\begin{align}\sin^4x+\cos^4x
&=(\sin^2x)^2+(\cos^2x)^2\\~\\
&=(\sin^2x+\cos^2x)^2-2\sin^2x\cos^2x\\~\\
&=(1)^2-2\sin^2x\cos^2x\\~\\
&=1 - 2\sin^2x\cos^2x\\~\\

\end{align}\]

Answer 3

factor out \(\sin^2x\)

Answer 4

I got it now! Thank you so much!

Answer 5

yw