If - y -2 - then cos-cos -cos -cos - y then is equal toA- 4 sin-2sin-2sin-2B- 4 sin-sin-sin- 4 cos-2cos-2cos-2D- 4 sin-2cos-2sin-2

The correct option is C cos(θ α)+cos(θ β)+cosθ+cos(θ γ) =2cos(θ (α+β/2)) cos(β γ/2)+2cos(γ 2)cos(θ γ 2) =2cos(γ 2)cos(β α/2) 2cos(γ/2)+cos(α+β 2) =2cos(γ 2)[c ...

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Byju's Answer

Standard XI

Mathematics

Trigonometric Ratios of Multiples of an Angle

If α+β+ y =2 ...

Question

If $α + β + γ = 2 θ, t h e n c o s θ + c o s (θ - α) + c o s (θ - β) + c o s (θ - γ)$ then is equal to

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Solution

The correct option is B

$c o s (θ - α) + c o s (θ - β) + c o s θ + c o s (θ - γ)$
= $2 c o s (θ - (\frac{α + β}{2})) c o s (\frac{β - γ}{2}) + 2 c o s (\frac{γ}{2}) c o s (θ - \frac{γ}{2})$
= $2 c o s (\frac{γ}{2}) c o s (\frac{β - α}{2}) 2 c o s (\frac{γ}{2}) + c o s (\frac{α + β}{2})$
= $2 c o s (\frac{γ}{2}) [c o s (\frac{β - α}{2}) + c o s (\frac{α + β}{2})]$
= $2 c o s (\frac{γ}{2}) 2 c o s \frac{γ}{2} c o s \frac{β}{2}$
$4 c o s \frac{α}{2} c o s \frac{β}{2} c o s \frac{γ}{2}$

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If α+β+γ=2θ, then cosθ+cos(θ−α)+cos(θ−β)+cos(θ−γ) then is equal to

The correct option is B cos(θ−α)+cos(θ−β)+cosθ+cos(θ−γ) =2cos(θ−(α+β2)) cos(β−γ2)+2cos(γ2)cos(θ−γ2) =2cos(γ2)cos(β−α2) 2cos(γ2)+cos(α+β2) =2cos(γ2)[cos(β−α2) +cos(α+β2)] =2cos(γ2) 2cosγ2cosβ2 4cosα2cosβ2cosγ2

If $α + β + γ = 2 θ, t h e n c o s θ + c o s (θ - α) + c o s (θ - β) + c o s (θ - γ)$ then is equal to