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Question

If 5tanθ=4, then find the value of 5sinθ3cosθsinθ+2cosθ

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Solution

tanθ=45=oppositesideadjacentsideΔABC is right angled at B,

C=θtanθ=ABBC=45

IfAB=4,BC=5

By Pythagoras theorem,

AC=AB2+BC2=41sinθ=441,cosθ=5415sinθ3cosθsinθ+2cosθ=5×4413×541441+2×541=514

1132698_1179952_ans_aa95b213604349ea94426d92fff6049b.png

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