- - Y are real numbers satisfying - y -The value of the given expression sin-sin-sin- isA- ZeroB- PositiveC- -3D- Negative

The correct option is B Positive Since sinα + sinβ + sinγ gt; sin(α + β + γ) When α + β + γ = π. ∴ sinα + sinβ + sinγ gt; 0 ∴ The value of sinα + sinβ ...

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Standard XII

Mathematics

Range of Trigonometric Expressions

α, β, Y are r...

Question

$α, β, γ$ are real numbers satisfying $α + β + γ = π$ .

The value of the given expression

$s i n α + s i n β + s i n γ$ is

Zero

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-3

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Positive

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Negative

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Solution

The correct option is C
Positive

Since $s i n α + s i n β + s i n γ$ > $s i n (α + β + γ)$

When $α + β + γ = π$ .

∴ $s i n α + s i n β + s i n γ$ > 0

∴ The value of $s i n α + s i n β + s i n γ$ is always positive.

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α,β,γ are real numbers satisfying α+β+γ=π. The value of the given expression sinα+sinβ+sinγ is

The correct option is C Positive Since sinα+sinβ+sinγ > sin(α+β+γ) When α+β+γ=π. ∴ sinα+sinβ+sinγ > 0 ∴ The value of sinα+sinβ+sinγ is always positive.

$α, β, γ$ are real numbers satisfying $α + β + γ = π$ .

The value of the given expression

$s i n α + s i n β + s i n γ$ is

The correct option is C
Positive

Since $s i n α + s i n β + s i n γ$ > $s i n (α + β + γ)$

When $α + β + γ = π$ .

∴ $s i n α + s i n β + s i n γ$ > 0

∴ The value of $s i n α + s i n β + s i n γ$ is always positive.