If sinθ + cosec θ = 4 , find the value of sin2θ + cosec2θ.
Answer & explanation
Correct answer: option 4
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