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Question

# If α,β,γ,δ are in arithmetic progression.Then sin(α+β+γ+δ) is equal to

A
sin(3β+δ)
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B
sin(α+3γ)
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C
sin(α+3δ)
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D
sin(3β+γ)
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Solution

## The correct options are A sin(3β+δ) B sin(α+3γ)As α,β,γ,δ is in A.P Let the common difference is r Then, β=α+r,γ=α+2r,δ=α+3r α+β+γ+δ=4α+6r A:3β+δ=3α+3r+α+3r=4α+6r⇒sin(3β+δ)=sin(4α+6r)=sin(α+β+γ+δ) B:α+3γ=α+3α+6r=4α+6r⇒sin(α+3γ)=sin(4α+6r)=sin(α+β+γ+δ) C:α+3δ=4α+9r,⇒sin(α+3δ)=sin(4α+9r)≠sin(α+β+γ+δ) D:3β+γ=4α+5r⇒sin(3β+γ)=sin(4α+5r)≠sin(α+β+γ+δ) Hence, options 'A' and 'B' are correct.

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