Question

if xcosteta=ycos(teta+2pie/3)=zcos(teta+4pie/3)then the value of 1/x+1/y+1/z=​

Answer 1

Hey there,

So we are given :

x cos θ = y cos(θ + 2π/3) = z cos(θ + 4π/3)

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To find : 1/x+1/y+1/z = ?

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So we :

Let x cos θ = y cos(θ + 2π/3) = z cos(θ + 4π/3) = k

k/x = cos θ

k/y = cos(θ + 2π/3)

k/z = cos(θ + 4π/3)

(k/x) + (k/y) + (k/z) = cos θ + cos(θ + 2π/3) + cos(θ + 4π/3)

k[(1/x) + (1/y) + (1/z)] = [cos θ + cos(θ + 4π/3)] + cos(θ + 2π/3)

Using the formula cos A + cos B = 2 cos(A + B)/2 cos(A – B)/2,

= 2 cos(θ + 2π/3) cos(-2π/3) + cos(θ + 2π/3)

= 2 cos(θ + 2π/3) (-1/2) + cos(θ + 2π/3)

= -cos(θ + 2π/3) + cos(θ + 2π/3)

= 0

Therefore , (1/x) + (1/y) + (1/z) = 0

HOPE THIS HELPS

THANKS