Mathematics

Mathematics

Problem

In △PQR\triangle PQR, angle QQ is a right angle. The sides are given by PQ=3kPQ = 3k, QR=4kQR = 4k and PR=5kPR = 5k, where kk is a positive real number. a. (i) Express sin⁡P\sin P, cos⁡P\cos P and tan⁡P\tan P in their simplest forms in terms of kk. b. (ii) If k=6k = 6, calculate the actual lengths of the three sides and verify the trigonometric ratios obtained in part (i). c. (iii) Prove algebraically that the value of tan⁡P\tan P is independent of the value of kk.

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