If x-cos-y-cos - -2-3 -z-cos - -2-3 - then x - y - z is equal to

The correct option is B 0We have #160; xcosθ=ycos ( θ #160;2π3 )= #160;zcos ( θ + #160;2π3 )=k #160; x+y+z=k(cosθ +cos ( θ 2π/3 )+cos ( θ ...

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Standard XII

Mathematics

Cos(A+B)Cos(A-B)

If x/cosθ=y...

Question

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 is equal to

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Solution

The correct option is B 0
We have $\frac{x}{cos θ} = \frac{y}{cos (θ - \frac{2 π}{3})} = \frac{z}{cos (θ + \frac{2 π}{3})} = k$
$x + y + z = k (cos θ + cos (θ - \frac{2 π}{3}) + cos (θ + \frac{2 π}{3})) = k \times 0$
Use formula for $cos x + cos y = 2 cos \frac{x + y}{2} cos \frac{x - y}{2}$
$\Rightarrow x + y + z = 0$
Hence, option 'B' is correct.

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Similar questions

Q. If

a = sin θ

b = sin (θ + 2 π / 3)

c = sin (θ + 4 π / 3)

x = cos θ

y = cos (θ + 2 π / 3)

z = cos (θ + 4 π / 3)

, then value of

Δ = ∣ ∣ ∣ ∣ \begin{matrix} a & b & c x & y & z b c & c a & a b \end{matrix} ∣ ∣ ∣ ∣

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

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

then x + y + z is equal to

Q. Let

tan (2 π | sin θ |) = cot (2 π | cos θ |)

, where

θ \in R

and

f (x) = (| sin θ | + | cos θ |)^{x}, x \geq 1

. Then range of

f (x)

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Q. If

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If xcosθ=ycos(θ−2π3)=zcos(θ+2π3) , then x + y + z is equal to

The correct option is B 0We have xcosθ=ycos(θ−2π3)=zcos(θ+2π3)=k x+y+z=k(cosθ+cos(θ−2π3)+cos(θ+2π3))=k×0Use formula for cosx+cosy=2cosx+y2cosx−y2⇒x+y+z=0Hence, option 'B' is correct.

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 is equal to