f(x)=sinx+sin3x+sin5x+…+sin15xcosx+cos3x+cos5x+…+cos15x then the value of f(x) at x=π32

sinα+sin(α+d)+….+sinα+(n-1)d==sinnd2sind2sinα+α+(n-1)d2andcosα+cos(α+d)+….+cos(α+(n-1)d)==sinnd2sind2cos(α+α+(n-1))d)2∴sinx+sin3x+….+sin15xcosx+cos3x+….+cos15x=sinx+15x2cosx+15x2=tan8x                                                    ∴fπ32=tan8π32=1