Question

If $3\sin x+4\cos ax=7$ has atleast one solution, then 'a' has to be necessarily _______.

• A. irrational number
• B. rational number
• C. even integer
• D. odd integer

Answer 1

The correct option is B rational number

$3\sin x+4\cos ax=7\therefore \sin x=1,\cos ax=1x=(4n_1+1)\frac{\pi }{2},ax=2n_2\pi ,n_1,n_2\in Z\therefore (4n_1+1)\frac{\pi }{2}=2\frac{n_2\pi }{a}\therefore a=\frac{4n_2}{4n_1+1}$
It is a rational number.