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Question

If tan θ=815, then the value of 17sinθ+5cosθ5tanθ+8sinθis

A
5941
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B
3541
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C
4159
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D
4135
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Solution

The correct option is C 4159
tanθ=815=perpendicularbase
Therefore
perpendicular=8
base=15
hypotenuse=perpendicular2+base2=82+152
hypotenuse=17 ...(i)
Hence sinθ=817 and cosθ=1517 ...(ii)
Substituting in the expression we get
17sinθ+5cosθ5tanθ+8sinθ
=8+17383+17
=4159
Hence answer is C

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