Answer the following questions about the tangent of a triple angle.

MATHEMATICS · Multi-part · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Answer the following questions about the tangent of a triple angle. (i) Derive an expression for

\tan 3x

involving only

\tan x

and constants (no other trigonometric functions). (ii) Using your result from part (i), determine all acute angles

x

(that is,

0<x<\dfrac{\pi}{2}

) for which

\tan 3x=1

. Give each answer in radians.