If-A-lies-in-the-third-quadrant-and-3-tan-A-4-0-then-5-sin-2A-3-sin-A-4cos-A-

Question Number 20435 by pp75718276@gmail.com last updated on 26/Aug/17

If A lies in the third quadrant and

3 \tan A - 4 = 0, then

5 \sin 2 A + 3 \sin A + 4 \cos A =

Answered by Tinkutara last updated on 27/Aug/17

\tan A = \frac{4}{3} \Rightarrow \sin A = \frac{- 4}{5}, \cos A = \frac{- 3}{5}

∵ π < A < \frac{3 π}{2}, both sine and cosine are

negative .

\sin 2 A = \frac{2 \tan A}{1 + \tan^{2} A} = \frac{\frac{8}{3}}{1 + \frac{16}{9}} = \frac{24}{25}

∴ 5 \times \frac{24}{25} - 3 \times \frac{4}{5} - 4 \times \frac{3}{5} = 0