If - - and y are in A-P- sin-sin y-cos y-cos- equals to-

The correct option is B cot β sinα sinγ/cosγ cosα =2sinα γ/2cosα+γ/2/2sinα γ/2sinα + γ/2 = cot(α + γ/2) = cot β [(α + γ/2) = β, because α, β, γ are in ...

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Byju's Answer

Standard XI

Mathematics

Sin(A+B)Sin(A-B)

If α, β and y...

Question

If $α$ , $β$ and $γ$ are in A.P, $\frac{s i n α - s i n γ}{c o s γ - c o s α}$ equals to .

tan

β

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cot

β

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tan

\frac{β}{2}

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cot

\frac{β}{2}

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Solution

The correct option is B cot $β$
$\frac{s i n α - s i n γ}{c o s γ - c o s α}$ $= \frac{2 s i n \frac{α - γ}{2} c o s \frac{α + γ}{2}}{2 s i n \frac{α - γ}{2} s i n \frac{α + γ}{2}} = c o t (\frac{α + γ}{2}) = c o t β$

$[(\frac{α + γ}{2}) = β, b e c a u s e α, β, γ a r e i n A . P .]$

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If α, β and γ are in A.P, sinα−sinγcosγ−cosα equals to .

The correct option is B cot β sinα−sinγcosγ−cosα =2sinα−γ2cosα+γ22sinα−γ2sinα+γ2=cot(α+γ2)=cot β [(α+γ2)=β,because α, β, γare in A.P.]

If $α$ , $β$ and $γ$ are in A.P, $\frac{s i n α - s i n γ}{c o s γ - c o s α}$ equals to .