Question

If 2SinA - CosA = 2 find SinA + 2CosA

Answer 1

Answer:

$2 \sin(x) - \cos(x) = 2 \\ \\ 2 \sqrt{2} ( \frac{1}{ \sqrt{2} } \sin(x) - \frac{1}{ \sqrt{2} }{ \cos(x) } ) = 2 \\ \\ \cos( \frac{\pi}{4} ) \sin(x) - \sin( \frac{\pi}{4} ) \cos(x) = \frac{2}{2 \sqrt{2} } \\ \\ \sin(x - \frac{\pi}{4} ) = \frac{1}{ \sqrt{2} } = \sin( \frac{\pi}{4} ) \\ \\ x - \frac{\pi}{4} = \frac{\pi}{4} \implies \: x = \frac{\pi}{2}$

So

$\sin(x) + 2 \cos(x) \\ \\ = \sin( \frac{\pi}{2} ) + 2 \cos( \frac{\pi}{2} ) \\ \\ = 1 + 2 \times 0 \\ = 1$

If it was only objective then it is very easy to guess that x is π/2 .