**Question**

**Introduction**

This is a bonus Maths II (rough equivalent
of Additional Mathematics syllabus) question from a test by Hwa Chong Institution (HCI) this year 2015. Independent schools in Singapore like
HCI are free to set their own curricula, but they usually end up covering slightly
more than the mainstream curriculum, since their students also take the
national examinations. For their internal
tests and exams, they can set bonus questions.
These are harder but optional questions that students can attempt and if
they are successful, the bonus marks can be added to their normal marks. It is also OK not to attempt the bonus
questions. That gives students the
choice and opportunity to stretch their minds, but they are not penalised if
they are unable to solve the bonus questions. In
this article, I present two approaches to tackling this question. Let us review some important formulas first.

**Some Useful Formulas**

**Solution 1**(via the Pythagorean Identity)

**Solution 2**(via

*R*-formula)

**Reflections / Extension**

Here is another HCI question on trigonometry that involves sine, cosine and tangent.

H04. Look for
pattern(s)

H05. Work
backwards

H09. Restate
the problem in another way

H10. Simplify
the problem

H11. Solve part
of the problem

H13* Use
Equation / write a Mathematical Sentence

**Suitable Levels**

*****GCE ‘O’ Level Additional Mathematics

* other syllabuses that involve trigonometry

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