Question

If sin thetha + cosec thetha =2 ,find the value of ( sin thetha square + cosec thetha square )

Answer 1

Given

sin∅ + cosec∅ = 2

To find

(sin²∅ + cosec²∅)

sin∅ + cosec∅ = 2

Square both the sides

(sin∅ + cosec∅)² = (2)²

⇒ sin²∅ + cosec²∅ + 2sin∅cosec∅ = 4

(using, (a + b)² = a² + b² + 2ab)

⇒ sin²∅ + cosec²∅ + 2 sin∅(1/sin∅) = 4

(since, cosec∅ = 1/sin∅)

⇒ sin²∅ + cosec²∅ + 2 = 4

⇒ sin²∅ + cosec²∅ = 2