Question : If $6 \cot heta=5$, then find the value of $\frac{(6 \cos heta+\sin heta)}{(6 \cos heta-4 \sin heta)}$
Option 1: 5
Option 2: 1
Option 3: 6
Option 4: 0

Question

Question : If $6 \cot heta=5$, then find the value of $\frac{(6 \cos heta+\sin heta)}{(6 \cos heta-4 \sin heta)}$

Option 1: 5

Option 2: 1

Option 3: 6

Option 4: 0

Team Careers360 · Accepted Answer

Correct Answer: 6

Solution : $6 \cot heta = 5$
⇒ $\cot heta = \frac{5}{6}$
Now, $\frac{(6 \cos heta+\sin heta)}{(6 \cos heta-4\sin heta)}$
Dividing numerator and denominator by $\sin heta$ in the above expression
⇒ $\frac{(6 \cos heta+\sin heta)}{(6 \cos heta-4\sin heta)}=\frac{(6\cot heta + 1)}{(6\cot heta-4)}$
$=\frac{6 imes \frac{5}{6} + 1}{6 imes \frac{5}{6}-4}$
$= \frac{5 + 1}{5-4}$
$=6$
Hence, the correct answer is 6.

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Question : If 6cot⁡θ=5, then find the value of (6cos⁡θ+sin⁡θ)(6cos⁡θ−4sin⁡θ)Option 1: 5Option 2: 1Option 3: 6Option 4: 0

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Question : If $6 \cot θ = 5$ , then find the value of $\frac{(6 \cos θ + \sin θ)}{(6 \cos θ - 4 \sin θ)}$
Option 1: 5
Option 2: 1
Option 3: 6
Option 4: 0