If sinθ + cosec θ = 5 , find the value of sin2θ + cosec2θ .
Answer & explanation
Correct answer: option 3
Formula I → [ cosec = \(\frac{1}{sinθ}\)]
Formula II → [If x + \(\frac{1}{x}\) = n and x2 + \(\frac{1}{x^2}\) = n2 - 2]
sinθ + \(\frac{1}{sinθ}\) = 5
⇒ sin2θ + \(\frac{1}{sin^2θ}\) = (5)2 - 2
⇒ sin2θ + cosec2θ = 25 - 2 = 23