Question

The equation $3\cos x+4\sin x=6$ has .............solution

• A. Finite
• B. Infinite
• C. One
• D. No

Answer 1

Answer: (D)

No

$3\cos x+4\sin x=6$

$a\cos x+b\sin x\in [-\sqrt{a^2+b^2}],\left[\sqrt{a^2+b^2}\right]$

here, $a=3$ and $b=4$

So,

$3\cos x+4\sin x\in [-5,5]$

So,

$3\cos x+4\sin xca{n}^{\prime }tgobeyond5$