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Question

# Assertion :The minimum value of the expression sinα+sinβ+sinγ where α,β,γ are real numbers such that α+β+γ=π is negative. Reason: If α+β+γ=π,then α,β,γ are the angles of a triangle.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution

## The correct option is C Assertion is correct but Reason is incorrectThe minimum value of the sum can be -3 provided sinα=sinβ=sinγ=−1 ⇒α=(4l−1)π/2, β=(4m−1)π/2, γ=(4n−1)π/2 Now α+β+γ=π⇒[4(l+m+n)−3]π/2=π ⇒4(l+m+n)=5 which is not possible as l, m, n are integers. 1. minimum value can not be -3. But for α=3π/2,β=3π/2,γ=2π,α+β+γ=π and sinα+sinβ+sinγ=−2 So sinα+sinβ+sinγ can have negative values and thus the minimum value of the sum is negative proving that statement-1 is correct. But the statement-2 is false as α+β+γ=π for α=β=2π/3,γ=−2π which are not the angles of a triangle.

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