COMEDK · Maths · 8. Trigonometric Ratios & Identities
\(\text { If } \dfrac{x}{\cos \theta}=\dfrac{y}{\cos \left(\theta+\dfrac{2 \pi}{3}\right)}=\dfrac{z}{\cos \left(\theta-\dfrac{2 \pi}{3}\right)} \text { then } x+y+z \text { is equal to }\)
- A \(-2\)
- B 1
- C \(-1\)
- D 0
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,…
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