Question

ysin^3α+xcos^3α=a,ysinα-xcosα=0,求证1/x²+1/y²=1/a&su

Answer 1

ysinα-xcosα=0

x=tanαy

x²=tan²αy²

1/x²=cot²α/y²

1/x²+1/y²

=(1+cot²α)/y²

=1/(sin²αy²) ①

又

ysin³α+xcos³α=a

ysin³α+tanαcos³α*y=a

ysin³α+ysinαcos²α=a

ysinα(sin²α+cos²α)=a

ysinα=a ②

所以

②代入①,得

1/x²+1/y²=1/a²

得证.