If 3 tan - -5- then 3 sin-5 cos -3 sin- -5 cos - is equal to

Given 3 tan θ =5, ⇒ tan θ =5/3 Consider 3 sinθ 5 cos θ/3 sinθ +5 cos θ =3 sinθ 5 cos θ/cosθ/3 sinθ+5 cos θ/cosθ (Dividing both numerator and denominator by co ...

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Standard IX

History

Machiavelli

If 3 tan θ =5...

Question

If $3 t a n θ = 5$ , then $\frac{3 s i n θ - 5 c o s θ}{3 s i n θ + 5 c o s θ}$ is equal to

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$\frac{5}{3}$

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$\frac{3}{5}$

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Solution

The correct option is B
0

Given $3 t a n θ = 5, \Rightarrow t a n θ = \frac{5}{3}$
Consider $\frac{3 s i n θ - 5 c o s θ}{3 s i n θ + 5 c o s θ}$
$= \frac{\frac{3 s i n θ - 5 c o s θ}{c o s θ}}{\frac{3 s i n θ + 5 c o s θ}{c o s θ}}$
(Dividing both numerator and denominator by $c o s θ$ )
$= \frac{3 t a n θ - 5}{3 t a n θ + 5} = \frac{3 \times \frac{5}{3} - 5}{3 \times \frac{5}{3} + 5} = 0$

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If 3tanθ=5, then 3sinθ−5cosθ3sinθ+5cosθ is equal to

The correct option is B 0 Given 3tanθ=5,⇒tanθ=53 Consider 3sinθ−5cosθ3sinθ+5cosθ =3sinθ−5cosθcosθ3sinθ+5cosθcosθ (Dividing both numerator and denominator by cosθ) =3tanθ−53tanθ+5=3×53−53×53+5=0

If $3 t a n θ = 5$ , then $\frac{3 s i n θ - 5 c o s θ}{3 s i n θ + 5 c o s θ}$ is equal to