Question

Question #c2150

Answer 1

`a=3/4, b=1/2`.

Explanation:

I hope, the Question is to express `y=sin^2x+cos^4x` as,

`y=a+(cos^2x-b)^2` using proper `a,b`.

Now, `a+(cos^2x-b)^2=y=ul(sin^2x)+cos^4x`,

`rArr a+(cos^4x-2bcos^2x+b^2)=ul(1-cos^2x)+cos^4x`.

`rArr color(red)((a+b^2))color(green)(-2b)cos^2x+cos^4x=color(red)1color(green)(-1)cos^2x+cos^4x`.

Comparing the respective co-effs., we have,

`color(red)(a+b^2=1), color(green)(-2b=-1)`

`:. b=(-1)/-2=1/2," and then, as "a=1-b^2=1-1/4=3/4`.