How to prove that a gaussian random variable multiplied by a deterministic sinusoid also results in a random variable with gaussian pdf? Suppose here A is a guassian random variable and B is given as below where fc is the frequency of sinusoid and t is the time. B=A∗cos(2π fc t). Is random variable B also gaussian. If so, how to prove it? This may be a foolish question and/ or direct one . But please help me, I cannot figure it out.