If x cos-y cos-2 -3-z cos-4 -3- then the value of 1-x-1-y-1-z is equal to

The correct option is B We have x cos θ=y cos ( θ+2 π/3 )=z cos ( θ+4 π/3 )=k ⇒ cos θ=k/x, cos ( θ+2 π/3 )=k/y and cos ( θ+4 π/3 )=k/z Hence k/x+k/y+k/z=co ...

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Byju's Answer

Standard XII

Mathematics

Sum of Trigonometric Ratios in Terms of Their Product

If x cosθ=y c...

Question

$I f x c o s θ = y c o s (θ + \frac{2 π}{3}) = z c o s (θ + \frac{4 π}{3}), t h e n t h e v a l u e o f \frac{1}{x} + \frac{1}{y} + \frac{1}{z} i s e q u a l t o$

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Solution

The correct option is C

We have

$x c o s θ = y c o s (θ + \frac{2 π}{3}) = z c o s (θ + \frac{4 π}{3}) = k \Rightarrow c o s θ = \frac{k}{x}, c o s (θ + \frac{2 π}{3}) = \frac{k}{y} a n d c o s (θ + \frac{4 π}{3}) = \frac{k}{z} H e n c e \frac{k}{x} + \frac{k}{y} + \frac{k}{z} = c o s θ + c o s (θ + \frac{2 π}{3}) + c o s (θ + \frac{4 π}{3})$
$= c o s θ + c o s (\frac{π}{3} - θ) - c o s (\frac{π}{3} + θ) = c o s θ - 2 c o s \frac{π}{3} c o s θ = 0$

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Similar questions

Q. If If

x c o s θ = y c o s (θ + \frac{2 π}{3}) = z c o s (θ + \frac{4 π}{3}),

then write the value of

\frac{1}{x} + \frac{1}{y} + \frac{1}{z}

If $x c o s θ = y c o s (θ + \frac{2 π}{3}) = z c o s (θ + \frac{4 π}{3})$ , prove that $x y + y z + z x = 0$

State the whether given statement is true or false

x cos θ = y cos (θ + \frac{2 π}{3}) = z cos (θ + \frac{4 π}{3})

,then

x y + y z + z x = 0

Q. If

\frac{x}{\cos θ} = \frac{y}{\cos (θ - \frac{2 π}{3})} = \frac{z}{\cos (θ + \frac{2 π}{3})},

then x + y + z = ____________.

Q. If

x, y, z

are non zero real numbers and if

x cos θ = y cos (θ + \frac{2 π}{3}) = z cos (θ + \frac{4 π}{3})

for some

θ \in R

, then show that

x y + y z + z x = 0

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If x cos θ=y cos (θ+2π3)=z cos(θ+4π3), then the value of 1x+1y+1z is equal to

The correct option is C We have x cos θ=y cos (θ+2π3)=z cos(θ+4π3)=k⇒cos θ=kx, cos(θ+2π3)=kyand cos(θ+4π3)=kzHence kx+ky+kz=cos θ+cos(θ+2π3)+cos(θ+4π3) =cos θ+cos(π3−θ)−cos(π3+θ)=cos θ−2 cosπ3cos θ=0

$I f x c o s θ = y c o s (θ + \frac{2 π}{3}) = z c o s (θ + \frac{4 π}{3}), t h e n t h e v a l u e o f \frac{1}{x} + \frac{1}{y} + \frac{1}{z} i s e q u a l t o$