Let $0, $0<\lambda<1, \mu=1-\lambda$. Does anyone see a good proof of the inequality:
$\sin(\lambda a)\sin(\lambda b)+\sin(\lambda a)\sin(\mu b)\cos(b)+\sin(\lambda b)\sin(\mu a)\cos(a)+\sin(\mu a)\sin(\mu b)>\sin(a)\sin(b).$
Let $0, $0<\lambda<1, \mu=1-\lambda$. Does anyone see a good proof of the inequality:
$\sin(\lambda a)\sin(\lambda b)+\sin(\lambda a)\sin(\mu b)\cos(b)+\sin(\lambda b)\sin(\mu a)\cos(a)+\sin(\mu a)\sin(\mu b)>\sin(a)\sin(b).$