Question

sin^4x+cos^4x=l+3+ksin^2xcos^2x then prove l-k=0

Answer 1

solution

sin⁴x+cos⁴x=I+3+ksin²x cos²x

=>(sin²x+cos²x)²-2 sin²x cos² x=I+3+ksin²x cos²x

=>1²-2sin²x cos²x =I+3+ksin²x cos²x

=>-2-2sin²x cos²x=I+ksin²x cos²x

comparing on both sides.....

I=-2

K=-2

therefore....

I-k=(-2)-(-2)=-2+2=O

therefore....

I-k=O

$\:\:\:\: \: \: \: \: \: \large\mathfrak{\underline{\huge\mathcal{\bf{\boxed{\boxed{\large\mathcal{I-K=0}}}}}}}$(proved)