Question

show that 1-2sin^2(X)*cos^2(X) =sin^4(X)+cos^4(X)

Answer 1

$RHS=sin^4x+cos^4x \\ =(sin^2x)^2+(cos^2x)^2$

=>(sin²x+cos²x)²-2sin²xcos²x   [Since (a²+b²)=(a+b)²-2ab]
=>1-2sin²xcos²x [ cos²x+sin²x=1]
=>LHS

hence proved

Answer 2

Step-by-step explanation:

$\begin{gathered}RHS=sin^4x+cos^4x \\ =(sin^2x)^2+(cos^2x)^2\end{gathered}$

RHS=sin 4 x+cos 4 x

=(sin 2 x) 2 +(cos 2 x) 2

=>(sin²x+cos²x)²-2sin²xcos²x [Since (a²+b²)=(a+b)²-2ab]

=>1-2sin²xcos²x [ cos²x+sin²x=1]

=>LHS

hence proved☑