The number of values of `theta` satisfying `4 cos theta+3 sin theta=5` as well as `3 cos theta + 4 sin theta = 5` is

Options

A. one
B. two
C. zero
D. none of these

Answer

C

Explanation

On adding given equations, we get
`7(cos theta+ sin theta)=10`
or `cos theta+ sin theta=10/7`
But maximum value of `cos theta+ sin theta=sqrt(1^(2)+1^(2))=sqrt(2) lt 10/7`.
So, no `theta` is possible.