Question

If $3\sin x+4\cos ax=7$ has at least one solution, then find the possible values of $a$.

• A. $a=\frac{5m}{5n+1}$
• B. $a=\frac{3m}{3n+1}$
• C. $a=\frac{2m}{2n+1}$
• D. $a=\frac{4m}{4n+1}$

Answer 1

The correct option is D $a=\frac{4m}{4n+1}$

We have $3\sin x+4\cos ax=7$ which is possible only when $\sin x=1$ and $\cos ax=1$

$x=(4n+1)\frac{\pi }{2}$ and $ax=2m\pi ;m,n\in Z$

$(4n+1)\frac{\pi }{2}=\frac{2m\pi }{a}$

$a=\frac{4m}{4n+1}$