If 5 tan θ = 4, then the value of is: ( { 5 \sin \theta - 3 \cos \theta }/ { 5 \sin \theta - 3 \cos \theta } )

SSC MTS Model Paper 6

Question : 32 of 150

Marks: +1, -0

If 5 tan θ = 4, then the value of is:

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

Solution:

5 \tan θ = 4 \tan θ = { 4 } /{ 5 } = { { Perpendicular } }/ { { Base } }

Now,

{ 5 \tan θ - 3 \cos θ } /{ 5 \sin θ + 3 \cos θ } = { 5 \tan θ - 3 }/ { 5 \tan θ + 3 }

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

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