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RRB Technician Grade I 19 Dec 2024 Shift 1 Paper

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Question : 17 of 100

Marks: +1, -0

If

\frac{18cos\theta +5sin\theta }{5cos\theta +4sin\theta }=2

, then find the value of cot θ.

$\frac{1}{3}$
$\frac{3}{5}$
$\frac{3}{8}$
$\frac{1}{7}$

Solution:

Concept:

Divide numerator and denominator by

\sin\theta

to convert the expression into

\cot\theta

, then solve the resulting linear equation.

Explanation:

Given:

\frac{18\cos\theta+5\sin\theta}{5\cos\theta+4\sin\theta}=2

.

Divide numerator and denominator by

\sin\theta

(assuming

\sin\theta \neq 0

):

\frac{18\cot\theta+5}{5\cot\theta+4}=2

.

Cross-multiply:

18\cot\theta+5=2(5\cot\theta+4)

.

Simplify:

18\cot\theta+5=10\cot\theta+8

.

Rearrange:

18\cot\theta-10\cot\theta=8-5

.

So

8\cot\theta=3

, hence

\cot\theta=\frac{3}{8}

.

Answer:

\cot\theta=\frac{3}{8}

, i.e., option C.

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