If `asinx+bcos(x+theta)+bcos(x-theta)=d ,` then the minimum value of `|costheta|` is equal to (a)`1/(2|b|)sqrt(d^2-a^2)` (b) `1/(2|a|)sqrt(d^2-a^2)` (c)`1/(2|d|)sqrt(d^2-a^2)` (d) none of these

Explanation

`asinx+b[2cosxcostheta]=d`

`asinx+(2bcostheta)cosx=d`

`|d|<=sqrt(a^2+(2bcostheta)^2`

`|d|<=sqrt(a^2+4b^2cos^2theta`

`d^2<=a^2+4b^2cos^2theta`

`(d^2-a^2)/(4b^2)<=cos^2theta`

`|costheta|>=sqrt(d^2-a^2)/(2|B|)`

Option A is correct.