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CBSE Class 12 Math 2009 Solved Paper

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Question : 1 of 29
Marks: +1, -0
Using principal value, evaluate the following: sin−1(sin3π5)
Solution:  
As sin−1 (sin θ) = θ so sin−1(sin(3π5)) = 3π5
But 3π5 ∉ [−π2,π2]
So,
sin−1(sin(3π5)) = sin−1(sin(π−2π5))
= sin−1(sin2π5)
= 2π5 ∊ [−π2,π2]
∴ Principal value is 2π5
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