If sinθ + cosec θ = 4 , find the value of sin2θ + cosec2θ.

15 18 16 14

14

Formula I → [ sinθ = \(\frac{1}{cosecθ}\)] Formula II → [If x + \(\frac{1}{x}\) = n and x2 + \(\frac{1}{x^2}\) = n2 - 2 ] sinθ + \(\frac{1}{sinθ }\) = 4 ⇒ sin2θ + \(\frac{1}{sin^2θ}\) = (4)2 - 2 ⇒ sin2θ + cosec2θ = 16 - 2 = 14