a+b=3-cos4x and a-b=4sin2x, then ab is always less or equal to?

 

Asked by aahnik.mohanty | 29th May, 2019, 07:58: PM

Expert Answer:

a + b = 3 - cos4x .....(i)
a - b = 4sin2x  ....(ii)
On squaring and subtracting (ii) from (i)
(a + b)2 - (a - b)2 = (3 - cos 4x)2 - 16sin2 2x
a2 + 2ab + b2 - a2 + 2ab - b2 = 9 - 6cos 4x + cos2 4x - 16sin2 2x
4ab = 9 - 6cos 4x + cos2 4x - 16sin2 2x
solving we get
ab = (1 + cos4x)2/4
Putting maximum value of cos 4x = 1
we get ab = 1

Answered by Sneha shidid | 30th May, 2019, 09:38: AM