If $α + β = 90°$ and $α = 2β,$ then the value of $cos^2α + sin^2β$ is :

$\frac{1}{3}$ $\frac{1}{5}$ 1 $\frac{1}{2}$

$\frac{1}{2}$

α + β = 90º    &     α = 2β 2β + β = 90º 3β = 90º  β = 30º    &   α = 2 × 30º = 60º Now, cos²α + sin²β = cos²60º + sin²30º = (\(\frac{1 }{2}\))² + (\(\frac{1 }{2}\))² = \(\frac{1 }{2}\)