2024 ACS(BR) P1 Q10

2024 ACS(BR) P1 Q10

Secondary 4
10 marks
  1. Prove the identity \(\dfrac{\cos x}{\mathrm{cosec}\,x-1}+\dfrac{\cos x}{\mathrm{cosec}\,x+1}=2\tan x\).[5]
  2. Solve the equation \(\tan x+2\sec^2x=5\) for \(0\le x\le2\pi\).[5]

Solution:

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Answer:(a) \(2\tan x\). (b) \(x=\dfrac\pi4,\ 2.16,\ \dfrac{5\pi}4,\ 5.30\) radians (non-exact values to 3 s.f.).

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