Question

If ${\cos }^{-1}x+co{s}^{-1}y=2\pi$, then find the value of $x^{100}+y^{200}+\frac{1}{x^{100}{y}^{200}}$

Answer 1

${\cos }^{-1}x+{\cos }^{-1}y=2\pi$

${\cos }^{-1}x+{\cos }^{-1}y=\pi +\pi$

${\cos }^{-1}x=\pi$ and ${\cos }^{-1}y=\pi$

$x=\cos \pi$ and $y=\cos \pi$

$x=-1$ and $y=-1$

$x^{100}+y^{200}+\frac{1}{(-1{)}^{100}(-1{)}^{200}}$

$1+1+\frac{1}{1}=3$