2025 TKSS PRELIMS P1 Q7

2025 TKSS PRELIMS P1 Q7

Secondary 4
7 marks
2025 Tanjong Katong Secondary School Prelims A Math Paper 1
  1. Find the value of \(k\) such that \(\sin(A+B)+\sin(A-B)=k\sin A\cos B\).[2]
  2. By letting \(P=A+B\) and \(Q=A-B\), show that
    \[\sin P+\sin Q=2\sin\left(\frac{P+Q}{2}\right)\cos\left(\frac{P-Q}{2}\right).\][2]
  3. Find the exact value of \(\sin75^\circ+\sin15^\circ\).[3]

Solution:

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Answer:(a) \(k=2\) (b) \(\sin P+\sin Q=2\sin\left(\frac{P+Q}{2}\right)\cos\left(\frac{P-Q}{2}\right)\) (c) \(\frac{\sqrt6}{2}\)

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