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Question: If \(\sin\theta + \text{cosec}\theta = 2\), then \(\sin^{2}\theta + \text{cose}\text{c}^{2}\theta =\...

If sin⁡θ+cosecθ=2\sin\theta + \text{cosec}\theta = 2, then sin⁡2θ+cosec2θ=\sin^{2}\theta + \text{cose}\text{c}^{2}\theta =

A

1

B

4

C

2

D

None of these

Answer

2

Explanation

Solution

sin⁡2θ+cosec2θ=(sin⁡θ+cosecθ)2−2sin⁡θ cosecθ\sin^{2}\theta + \text{cose}\text{c}^{2}\theta = (\sin\theta + \text{cosec}\theta)^{2} - 2\sin\theta\text{ cosec}\theta

=(2)2−2=4−2=2,= (2)^{2} - 2 = 4 - 2 = 2, since(sin⁡θ+cosecθ)=2.(\sin\theta + \text{cosec}\theta) = 2.