If sin-sin-sin y-0-cos-cos-cos y then value of cos -cos -cos - is

The correct option is A (sin α+sin β)^2+(cos α + cos β)^2=(1 sin γ)^2+(1 cosγ)^2 ⇒ 1+1+2 cos(α β)=1 ⇒ 1 cos (α β)= 1/2 Similarly cos(β γ)= 1/2 and cos ...

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Byju's Answer

Standard XII

Mathematics

Conditional Identities

If sinα+sinβ+...

Question

$I f s i n α + s i n β + s i n γ = 0 = c o s α + c o s β + c o s γ$ then value of $c o s (α - β) + c o s (β - γ) + c o s (γ - α) i s$

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Solution

The correct option is A

$(s i n α + s i n β)^{2} + (c o s α + c o s β)^{2} = (1 - s i n γ)^{2} + (1 - c o s γ)^{2} \Rightarrow 1 + 1 + 2 c o s (α - β) = 1 \Rightarrow 1 c o s (α - β) = \frac{- 1}{2} S i m i l a r l y c o s (β - γ) = \frac{- 1}{2} a n d c o s (γ - α) = \frac{- 1}{2}$

$∴$ Thus the value of expression is $\frac{- 3}{2}$

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Similar questions

Q. If

a = cos α + i sin α, b = cos β + i sin β,

c = cos γ + i sin γ

and

\frac{a}{b} + \frac{b}{c} + \frac{c}{a} = 1,

then

If $cos (α - β) + cos (β - γ) + cos (γ - α) = - \frac{3}{2}$ , Prove
that $cos α + cos β + cos γ = sin α + sin β + sin γ = 0$

cos (α - β) + cos (β - γ) + cos (γ - α) = - \frac{3}{2}

then prove that

cos α + cos β + cos γ = sin α + sin β + sin γ = 0

Q. If

cos (α - β) + cos (β - γ) + cos (γ - α) = - \frac{3}{2}, cos α + cos β + cos γ = p & sin α + sin β + sin γ = q

, then

Q. Assertion :If

c o s (β - γ) + c o s (γ - α) + c o s (α - β) = - \frac{3}{2}

, then Reason:

c o s α + c o s β + c o s γ = 0

and

s i n α + s i n β + s i n γ = 0

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If sin α+sin β+sin γ=0=cos α+cos β+cos γ then value of cos(α−β)+cos(β−γ)+cos(γ−α) is

The correct option is A (sin α+sin β)2+(cos α+cos β)2=(1−sinγ)2+(1−cosγ)2⇒1+1+2 cos(α−β)=1⇒1 cos (α−β)=−12Similarly cos(β−γ)=−12 and cos(γ−α)=−12 ∴ Thus the value of expression is −32

$I f s i n α + s i n β + s i n γ = 0 = c o s α + c o s β + c o s γ$ then value of $c o s (α - β) + c o s (β - γ) + c o s (γ - α) i s$