Question

If 4 tanθ = 3, find the value of (3 sinθ-4cosθ)/(3 sinθ+4cosθ)​

Answer 1

Answer:

Answer

We have,

3sinθ+4cosθ=5              ………. (1)

On squaring both sides, we get

(3sinθ+4cosθ)2=52

9sin2θ+16cos2θ+24sinθcosθ=25

9(1−cos2θ)+16(1−sin2θ)+12×2sinθcosθ=25

9−9cos2θ+16−16sin2θ+12×2sinθcosθ=25

25−9cos2θ−16sin2θ+12×2sinθcosθ=25

9cos2θ+16sin2θ−12×2sinθcosθ=0

(3cosθ−4sinθ)2=0

3cosθ−4sinθ=0

Hence, the value is 0.

Answer 2

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