Question

If $(a+2)\sin \alpha +(2a-1)\cos \alpha =(2a+1)$, the $\tan \alpha =$

• A. $3/4$
• B. $4/3$
• C. $\frac{2a}{a^2+1}$
• D. $\frac{2a}{a^2-1}$

Answer 1

Answer: (B)

$4/3$

Simplifying $\left(a+2\right)\sin \alpha +\left(2a-1\right)\cos \alpha =2a+1$

$a\sin \alpha +2\sin \alpha +2a\cos \alpha -\cos \alpha =2a+1$

$a\left(\sin \alpha +2\cos \alpha \right)+2\sin \alpha -\cos \alpha =2a+1$

$\sin \alpha +2\cos \alpha =2$

$2\sin \alpha -\cos \alpha =1$

$\cos \alpha =\frac{3}{5},\sin \alpha =\frac{4}{5}$

$\tan \alpha =\frac{\frac{4}{5}}{\frac{3}{5}}$

$\tan \alpha =\frac{4}{3}$