This is the first time I'm posting here. If you can also tell me how to format this like a pro, I'll be very grateful.
1st question:
Prove the following inequality: $$0^{\circ} < a, b, c < 180^{\circ}$$
$$\sin a \times \sin b \times \sin c \le \sin\left(\frac{a+b}{2}\right) \times \sin\left(\frac{a+c}{2}\right) \times \sin\left(\frac{a+b}{2}\right)$$
2nd question:
Prove the following inequality: $$a + b + c = 90^{\circ}$$
$$\sin a \times \sin b \times \sin c \le \frac{1}{8}$$