If `f(x)=2(7cos x +24 sin x) (7 sinx -24 cos x)`, for even `x in R` then maximum value of f(x) is __________

Answer

625

Explanation

`f(x) = 2(7 cos x + 24 sin x ) (7 sinx - 24 cos x )`
Let `r cos theta = 7 , r sin theta = 24`
`therefore r ^(2) = 625 , tan theta = (24)/(7)`
`therefore f(x) = 2rcos (x- theta) xx r sin (x- theta)`
`= r^(2) ( sin 2 (x - theta))`
`f(x)_(max)= 25^(2)`