[IB-HL H&H_Ex13e] pg 374 Q19 Angles with nice tans add up nicely

Question

This is taken from Haese and Harris textbook for IB Mathematics page 374.  It involves an interesting connection between certain angles whose tangents are nice fractions and the 45º degree angle i.e. ^p/₄.

Solution

Here is another look at the problem.

Suitable Levels

* GCE ‘O’ Level Additional Mathematics

* revision for GCE ‘A’ Level H2 Mathematics

* revision for IB Mathematics HL / SL

* other syllabuses that teach further trigonometry