Question

If sinθ + cosecθ = 2, find the value of sin² θ + cosec² θ

Answer 1

The value of sin²θ + cosec²θ is 2.

• Given,

sin θ  + cosec θ  = 2

• Squaring both the sides, we get,

(sin θ  + cosec θ )² = 2²

Or, sin²θ + cosec²θ + 2. sin θ. cosec θ = 4     { Applying (a + b)² = a² + b² + 2ab }

Or, sin²θ  + cosec²θ  + 2 . 1 = 4     (sin θ . cosec θ  = sin θ . (1/sin θ ) = 1 )

Or, sin²θ  + cosec²θ + 2 = 4

Or, sin²θ  + cosec²θ = 4 - 2

Or, sin²θ  + cosec²θ  = 2

•Therefore, sin²θ + cosec²θ = 2

Answer 2

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