Question

If 5 tan θ = 4, find the value of : (8 sinθ – 3cosθ) /(8 sinθ + 2 cosθ)

Answer 1

5 tanθ = 4

=> tanθ = 4/5 = P/B

=>sinθ = 4/√41 , cosθ = 5/√41

Put the values of sinθ and cosθ in the equation to find the answer.

(8sinθ-3 cosθ)/(8sinθ+2cosθ)

= (8×4/√41-3×5/√41)/(8×4/√41+2×5/√41)

= (32-15)/(32+10)

= 17/42