Mathematics

Mathematics

Problem

In right triangle PQR, ∠Q=90∘\angle Q = 90^\circ and the hypotenuse PR=15 cmPR = 15\,\text{cm}. If PQ=9 cmPQ = 9\,\text{cm}, let θ=∠P\theta = \angle P. Another acute angle ϕ\phi is such that cos⁡ϕ=sin⁡θ\cos \phi = \sin \theta. a. (i) Calculate sin⁡θ\sin \theta, cos⁡θ\cos \theta and tan⁡θ\tan \theta. b. (ii) Find sin⁡ϕ\sin \phi and tan⁡ϕ\tan \phi. c. (iii) Show that tan⁡θ×tan⁡ϕ=1\tan \theta \times \tan \phi = 1.

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