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ITMC 2018 Grade 11 National Preliminary set01 Question 29

ITMC · ITMC 2018 Grade 11 National Preliminary set01

Question 29

If the answer is not an integer, give the nearest integer. If the calculated answer has more than five digits, give its last five digits.

Let $\theta\in[0,\pi/2]$ and $\cos2\theta=1/8$. Write $\cos3\theta+\cos\theta=a/b$ for coprime positive integers $a,b$. Find $a+b$.