<s>[INST] Given $3\cos x - 4 \sin x = 2$, find $3 \sin x + 4 \cos x$ without first solving for $x$ If $$3\cos{x}-4\sin{x}=2$$
find $$3\sin{x} +4\cos{x} $$
I have solved the equation for $x$, then calculated the required value, but I think there is a direct solution without solving the equation.
 [/INST] Hint:
Using Brahmagupta-Fibonacci Identity,
$$(a\cos x-b\sin x)^2+(a\sin x+b\cos x)^2=(a^2+b^2)(\cos^2x+\sin^2x)=?$$
</s>