**Question**

This
problem appears as problem 58 from a Facebook group and it is set by Kunihiko
Chikaya. Ordinary integration problems are
already challenging, but this one is tough on steroids.

**The Standard Approach**

**Solution 1**

With this result, I realised that there is a short
cut. We can make use of symmetry. Note that
sin(

*p*–*x*) = sin*x*and cos(*p*–*x*) = - cos*x*.**Solution 2**

H04. Look for
pattern(s): “onions”, exploit
symmetry

H05. Work
backwards

H09. Restate
the problem in another way

H10. Simplify
the problem

H11. Solve part
of the problem

**Suitable Levels**

*****University / College Mathematics

*****challenge for ‘A’ Level H2 Mathematics

*****challenge for IB HL Mathematics

* other syllabuses that involve
trigonometry and integration

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