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Question
If sinθ + cosecθ = 2, then sin2θ + cosec2θ is equal to ______.
Options
1
4
2
None of these
Solution
If sinθ + cosecθ = 2, then sin2θ + cosec2θ is equal to 2.
Explanation:
sinθ + cosecθ = 2
Squaring L.H.S and R.H.S
We get,
⇒ (sinθ + cosecθ)2 = 22
⇒ (sinθ + cosecθ)2 = 4
⇒ sin2θ + cosec2θ + 2sinθ cosecθ = 4 [∵ `1/sintheta = cosectheta`]
= sin2θ + cosec2θ + 2 = 4
= sin2θ + cosec2θ = 2
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