How do you solve the second question?….........................

the above inequality is equivalent to proving the following inequality:
sina(1 – cos(c+b))+sinb(1 – cosacosc)+sinc(1 – cosacosb) > 0 [merely exapnsion of given terms]

 

obviously sina(1 – cos(c+b)) is greater than zero

sinb(1 – cosacosc) is greater than zero

sinc(1 – cosacosb) is greater than zero, as long as a b c are in 0 to pi/2.

hence adding all these inequalities we get the required inequality.