Question

If a+b= pi/2, prove that the maximum value of cosacosb 1/2

Answer 1

Note:
a+b ≥ a or ≥ b
=> pi/2 ≥ a or ≥b

Now, a+b = pi/2
=> sin a = cosb
=>cosa cosb = sinbcosb = 2sinbcosb /2 
= sin 2b /2 ≥ 1/2

Therefore, minimum value is 1/2