The value of (3 tan 10° - tan^3 10°)/(1 - 3 tan^2 10°) is: (a) 1/√3 (b) 1/2 (c) √3/2 (d) 1/√2

Question

The value of \(\frac{3tan10°-tan^310°}{1-3tan^210°}\) is:

(a) \(\frac{1}{\sqrt{3}}\)

(b) \(\frac{1}{2}\)

(c) \(\frac{\sqrt{3}}{2}\)

(d) \(\frac{1}{\sqrt{2}}\)

Answer 1

(a) \(\frac{1}{\sqrt{3}}\)

\(\frac{3tan10°-tan^310°}{1-3tan^210°}\) = tan(3 x 10°) [∵ tan 3A = \(\frac{3tanA-tan^3A}{1-3tan^2A}\)]

= tan 30°

= \(\frac{1}{\sqrt{3}}\)