Mathematics

Mathematics

Problem

If sec⁡θ+tan⁡θ=5\sec \theta+\tan \theta=5 with 0<θ<π20<\theta<\dfrac{\pi}{2}, (a) Prove that sec⁡θ−tan⁡θ=15\displaystyle \sec \theta-\tan \theta=\dfrac15. (b) Hence, or otherwise, determine the exact values of sin⁡θ\sin \theta, cos⁡θ\cos \theta, tan⁡θ\tan \theta, cot⁡θ\cot \theta, sec⁡θ\sec \theta and csc⁡θ\csc \theta, rationalising denominators wherever required.

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