Suppose that h(ω) is the fourier sine transform of h(x) and h(ω) = s(ω) c(ω), where s(ω) and c(ω) are the fourier sine and cosine transforms of s(x) and c(x), respectively. show that h(x) = 1 π ∫ [infinity] 0 s(x¯)[c(x − x¯) − c(x + x¯)] dx¯ = 1 π ∫ [infinity] 0 c(x¯)[s(x + x¯) − s(x¯ − x)] dx. ¯ (b) suppose that h(ω) is the fourier cossine transform of h(x) and h(ω) = f(ω) g(ω), where f(ω) and g(ω) are the fourier cosine transforms of f(x) and g(x), respectively. show that h(x) = 1 π ∫ [infinity] 0 g(x¯)[f(x − x¯) + f(x + x¯)] dx. ¯ note that, in this result, f and g can be interchanged.