First slide

Trigonometric Identities

Question

If 3 tan A+ 4=0,thenthe value of 2 cotA-5 cos A+ sinA is equal to

Moderate

A

$\frac{23}{10} if \frac{π}{2} < A < π$
B

$\frac{23}{10} if \frac{3 π}{2} < A < 2 π$
C

$\frac{- 53}{10} if \frac{π}{2} < A < π$
D

$\frac{- 53}{10} if \frac{3 π}{2} < A < 2 π$

Solution

We have $\tan A = - \frac{4}{3}$
lf A lies in 2^nd quadrant, then
$\sin A = \frac{4}{5}, \cos A = \frac{- 3}{5}, and \cot A = \frac{- 3}{4}$
If A lies in 4^th quadrant, then
$\sin A = \frac{- 4}{5}, \cos A = \frac{3}{5} and \cot A = \frac{- 3}{4}$

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