If <span class="math-tex">\(\rm \frac{\tan x}{2}= \frac{\tan y}{3} = \frac{\tan z}{5}\)</span> and x + y + z = π, then the value of tan<sup>2</sup> x + tan<sup>2</sup> y + tan<sup>2</sup> z is:
Let \(\tan x = 2k\), \(\tan y = 3k\), \(\tan z = 5k\).
Since \(x + y + z = \pi\): \(\tan x + \tan y + \tan z = \tan x\tan y\tan z\).
\(10k = 30k^3 \Rightarrow k^2 = \frac{1}{3}\)
\(\tan^2 x + \tan^2 y + \tan^2 z = (4 + 9 + 25)k^2 = \frac{38}{3}\)
Answer: (A) \(\frac{38}{3}\)
Reinforce your conceptual grasp with related questions from NIMCET 2018:
Take timed full-length mock tests with authentic question distributions, negative marking (+12/-3 in Math), and instant All India Rank calculation.
Start Free Mock Test Series →