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Question
If 3 cos θ = 5 sin θ, then the value of
Options
\[\frac{271}{979}\]
\[\frac{316}{2937}\]
\[\frac{542}{2937}\]
None of these
Solution
`bb(271/979)`
We have,
`3 cos θ=5 sin θ`
So we can manipulate it as,
`tan θ=3/5`
So now we can get the values of other trigonometric ratios,
`sin θ=3/sqrt34`
`cos θ=5/sqrt34`
`sec θ=sqrt34/5`
So now we will put these values in the equation,
=`( 5 sin θ-2 sec^3 θ+2 cos θ)/(5 sin θ-2 sec^3 θ-2 cos θ)`
`=(5(3/sqrt34)-2((34sqrt34)/125)+10/sqrt34)/(5(3/sqrt34)+2((34sqrt34)/125)-10/sqrt34)`
`=((15)(125)-(2)(34)^2+1250)/((15)(125)+(2)(34)^2-1250)`
`= (1875 - 2312 + 1250)/(1875 + 2312 - 1250)`
`= 813/2937`
`=271/979`
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