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Question

If 12cscθ=13, find the value of 2sinθ9cosθ4sinθ9cosθ.

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Solution

12cosecθ=13cosecθ=1312(1)weknowthatcosecx=hp(2)comparing(1)and(2)wegeth=13kandp=12kb=h2p2=(13k)2(12k)2=5ksinθ=ph=1213andcosθ=bh=513now,2sinθ9cosθ4sinθ9cosθ=2.12139.5134.12139.513=7

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