If sin(π cos θ) = cos(π sin θ), then θ isयदि sin(π cos θ) = cos(π sin θ), तो θ है

Explanation

cos(π sin θ) = sin(π/2 + π sin θ), so π cos θ = π/2 + π sin θ, i.e. cos θ − sin θ = 1/2. Squaring gives 1 − sin 2θ = 1/4, so sin 2θ = 3/4 and θ = (1/2) sin⁻¹(3/4).cos(π sin θ) = sin(π/2 + π sin θ), इसलिए π cos θ = π/2 + π sin θ, अर्थात् cos θ − sin θ = 1/2। वर्ग करने पर 1 − sin 2θ = 1/4, अतः sin 2θ = 3/4 और θ = (1/2) sin⁻¹(3/4)।