Question

If $3\sin x+4\cos ax=7$ has at least one solution, then 'a' has to be necessarily a/an :

• A. Odd Integer
• B. Even Integer
• C. Rational Number
• D. Irrational Number

Answer 1

Answer: (C)

Rational Number

Given,

$3sinx+4cosax=7$

The solution is possible when,

$sinx=1$

$x=si{n}^{-1}\left(1\right)=\frac{\pi }{2}$

$cosax=1$

$ax=co{s}^{-1}\left(1\right)=2\pi n$

$a=\frac{2\pi n}{\frac{\pi }{2}}=4n$

$a=4,8,12,\mathrm{16......}$

All are rational number.

The correct option is C.