Question
If a sinx + b cos(x+θ) + b cos(x-θ) = d, then the minimum value of |cos θ| is equal to :
sir i have expanded cos(x+θ) & cos(x-θ) and after that i got the equation: (d sec x - a tanx)/2b = cos θ. now , can i write minimum value of (d sec x -a tanx) = (d²-a²)^(1/2).. as all the options contain (d²-a²)^(1/2).......or do tell the other hint to solve it..
Dear amit your starting steps are correct
now let us consider that d secx - a tanx = y
on differentiating we will get d secx tanx - a sec2x = dy/dx
on comparing with 0 we get d tanx = a secx or sinx = a/d so secx = d/√(d2-a2) and tanx = a/√(d2-a2)
so minimum of given expression = [d2/ √(d2-a2)] - [a2/√(d2-a2)] = √(d2-a2)