Math Problem 5

(ai) Express \(\tan 3A\) in terms of \(\tan A\).

(aii) Prove that \(\tan A\ \tan\left(\frac{\pi}{3}+A\right)\tan\left(\frac{2\pi}{3}+A\right)= -\tan 3A.\)

(b) Solve the equation \(\tan\left(\frac{\pi}{4}+x\right) \tan\left(\frac{7\pi}{12}+x\right) \tan\left(\frac{11\pi}{12}+x\right) =-1,\) where \(0 < x < \frac{\pi}{4}\).

($2 + 3 + 3$ marks)

Suggested Solution

why am I torturing myself by doing this

and also yes I used a paper to do the question instead of the usual digital annotation 💩