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Question

Question 12
If 4tanθ=3, then (4sinθcosθ4sinθ+cosθ) is equal to

(A) 23
(B) 13
(C) 12
(D) 34

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Solution

The answer is (C).

Given, 4tanθ=3

tanθ=34 ..........(i)

4sinθcosθ4sinθ+cosθ=4sinθcosθ14sinθcosθ+1

[divide by cosθ in both numerator and denominator]

=4tanθ14tanθ+1 [tanθ=sinθcosθ]

=4(34)14(34)+1=313+1=24=12 [put the value from Eq.(i)]

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