Question
If tan θ = 8/3 , then the value of (3Sinθ+2
Cosθ )/(3 Sinθ-2Cosθ) isSolution
(3Sinθ+2 Cosθ )/(3 Sinθ-2Cosθ) By dividing numerator and denominator by cosθ (3 × Sinθ/Cosθ+2 × Cosθ/Cosθ)/(3 × Sinθ/Cosθ-2 × Cosθ/Cosθ) = (3 tanθ+2)/(3 tanθ-2) Put the value of Tanθ = (3 × 8/3+2)/(3 × 8/3-2) = (8+2)/(8-2) = 10/6 = 5/3 Alternate Solution: sinθ/Cosθ = 8/3 So by putting Sinθ=8 & Cosθ = 3 in the required ratio, We will get (3Sinθ+2 Cosθ )/(3 Sinθ-2Cosθ) = (3*8+2*3)/ (3*8 - 2* 3 ) = 30/ 18 = 5/3
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