The correct option is A \N
Here, the equation is of the form a cosθ+b sinθ=c.
Now, dividing the equation by √a2+b2=√32+42=5 on both sides, we get the equation as:
35 sinθ+45 cosθ=65.
Now, we can write the equation as:
which is not possible as cos θ∈(−1, 1].Thus, the equation has no real roots.