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in Trigonometry by (51.1k points)
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If 3 tan θ = 4 then (3sin θ + 2cos θ)/(3sin θ – 2cosθ) = ?

(A) 2

(B) 3

(C) 4

(D) 5

1 Answer

+1 vote
by (48.4k points)
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Best answer

The correct option is (B) 3.

3tan θ = 4

tan θ = 4/3

Given expression

= (3sin θ + 2cos θ)/(3sin θ – 2cosθ)

= (3tan θ + 2)/(3tan θ – 2)   [dividing num. and denom. By cos θ]

= (3 x 4/3 + 2)/(3 x 4/3 – 2)

= (4 + 2)/(4 – 2)

= 6/2

= 3

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