First slide

Trigonometric Identities

Question

If A lies in the second quadrant and $3 \tan A + 4 = 0,$ then the value of $2 \cot A - 5 \cos A + \sin A$ is equal to

Moderate

A

$- \frac{53}{10}$
B

$\frac{23}{10}$
C

$\frac{37}{10}$
D

$\frac{7}{10}$

Solution

Using right angled triangle, we have
$\tan A = - \frac{4}{3} \Rightarrow c o t A = - \frac{3}{4}, \cos A = - \frac{3}{5} a n d \sin A = \frac{4}{5} ∴ 2 \cot A - 5 \cos A + \sin A = - \frac{3}{2} + 3 + \frac{4}{5} = \frac{23}{10}$

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