If a = ^ - 1 ( (5)) and b = ^ - 1 ( (5)) , then a ^ 2 + b ^ 2 is...

Given: $a = \sin^{- 1}\left(\sin \left(5\right)\right)\text{and}b = \cos^{- 1}\left(\cos \left(5\right)\right)$

$⇒ a = 5 - 2\pi\text{and}b = 2\pi - 5$

$⇒ {a}^{2} + {b}^{2} = {\left(5 - 2\pi\right)}^{2} + {\left(2\pi - 5\right)}^{2}$

$⇒ {a}^{2} + {b}^{2} = 25 + 4{\pi}^{2} - 20\pi + 4{\pi}^{2} + 25 - 20\pi$

$⇒ {a}^{2} + {b}^{2} = 8{\pi}^{2} - 40\pi + 50$