Question

If 3 cos θ = 5 sin θ, then the value of

\[\frac{5 \sin \theta - 2 \sec^3 \theta + 2 \cos \theta}{5 \sin \theta + 2 \sec^3 \theta - 2 \cos \theta}\] is?

पर्याय

• \[\frac{271}{979}\]

• \[\frac{316}{2937}\]

• \[\frac{542}{2937}\]

• None of these

Answer 1

`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`