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COMEDK · Maths · 8. Trigonometric Ratios & Identities

\(\text { If } \dfrac{x}{\cos \theta}=\dfrac{y}{\cos \left(\theta+\dfrac{2 \pi}{3}\right)}=\dfrac{z}{\cos \left(\theta-\dfrac{2 \pi}{3}\right)} \text { then } x+y+z \text { is equal to }\)

  1. A \(-2\)
  2. B 1
  3. C \(-1\)
  4. D 0
Verified Solution

Answer & Solution

Correct Answer

(D) 0

Step-by-step Solution

Detailed explanation

Let \(\dfrac{x}{\cos \theta} = \dfrac{y}{\cos(\theta + \dfrac{2\pi}{3})} = \dfrac{z}{\cos(\theta - \dfrac{2\pi}{3})} = k\). Then \(x = k \cos \theta\), \(y = k \cos(\theta + \dfrac{2\pi}{3})\), and \(z = k \cos(\theta - \dfrac{2\pi}{3})\). Summing these values,…