Question

If n is the number of solutions of the equation 2cos x(4sin(π/4+x)sin(π/4-x)-1)=1,x∈[0, π] and S is the sum of all these solutions, then the ordered pair (n, S) is :

(1) (3,13π/9)

(2) (2,2π/3) 

(3) (2,8π/9) 

(4) (3,5π/3)

Answer 1

Option : (1).(3,13π/9)

2cos x(4sin(π/4+x)sin(π/4-x)-1) = 1