C-09-Q211mediumsingle_mcqIf p+q=2p + q = \sqrt{2}p+q=2 (with p=sinθp = \sin\thetap=sinθ, q=cosθq = \cos\thetaq=cosθ, θ\thetaθ acute), then θ=?\theta = ?θ=?a30∘30^\circ30∘b45∘45^\circ45∘c60∘60^\circ60∘d75∘75^\circ75∘ব্যাখ্যাsinθ+cosθ=2\sin\theta+\cos\theta=\sqrt2sinθ+cosθ=2 holds when sinθ=cosθ=12\sin\theta=\cos\theta=\dfrac{1}{\sqrt2}sinθ=cosθ=21, which occurs at the acute angle θ=45∘\theta=45^\circθ=45∘.