If 5tanθ = 4, then find the value of ( { 5 \sin \theta - 3 \cos \theta}/ { 5 \sin \theta + 3 \cos \\theta } )

SSC MTS Model Paper 2

Question : 37 of 150

Marks: +1, -0

If 5tanθ = 4, then find the value of

( { 5 \sin θ - 3 \cos θ}/ { 5 \sin θ + 3 \cos \θ } )

Solution:

(3)

5 \tan θ = 4 ⇒tan θ = { 4 } /{ 5 }

\therefore { 5 \sin θ - 3 \cos θ }/ { 5 \sin θ + 3 \cos θ} = { { 5 \sinθ - 3 \cosθ }/ { \cos θ } }/ { { 5 \sin θ + 3 \cos θ }/ { \cos θ } }

= { 5 \tan θ - 3 }/ { 5 \tan θ + 3 } = { 5 × { 4 } /{ 5 } - 3 }/ { 5 × { 4 }/ { 5 } + 3 } = \ { 4 - 3 } /{ 4 + 3 } = { 1 }/ { 7 }

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