Question
Download Solution PDFIf \(\rm \frac{x}{\cos \theta}=\frac{y}{\cos \left(\frac{2\pi}{3}-\theta\right)}=\frac{z}{\cos\left(\frac{2\pi}{3}+\theta\right)}\) then what is x + y + z equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
⇒ \(\rm \frac{x}{\cos θ}=\frac{y}{\cos \left(\frac{2\pi}{3}-θ\right)}=\frac{z}{\cos\left(\frac{2\pi}{3}+θ\right)}\) = k (say)
⇒ x = kcosθ
⇒ y = k \(cos\frac{2\pi }{3} -θ \)
⇒ z = k \(cos\frac{2\pi }{3} +θ \)
Now, x + y + z = k [cosθ + cos \((\frac{2\pi }{3} -θ) + cos(\frac{2\pi }{3} +θ)\)]
= k [cosθ + 2cos\(\frac{2\pi }{3}cosθ \)]
= k[cosθ + 2 (\(-\frac{1}{2}) cosθ \)]
= k[cosθ- cosθ ] =0
⇒ x + y + z =0
∴ Option (b) is correct.
Last updated on May 30, 2025
->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.
-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.