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

The correct option is B 0 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 nume ...

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Byju's Answer

Standard IX

Mathematics

Relationship between Trigonometric Ratios

If 3 tanθ=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

$\frac{3}{5}$

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$\frac{5}{3}$

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Solution

The correct option is D
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

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