(x sin x+cos x)(x cos x-sin x)

If y=(sin x-x cos x)(cos x+x sin x), show that (dy)/(dx)=x sin2x-x^(2)cos2x

If sin(sin x+cos x)=cos(cos x-sin x) then the largest possible value of sin x, is

(sin x+x cos x)/(x sin x-cos x)

2tan2x = (cos x + sin x) / (cos x-sin x) - (cos x-sin x) / (cos x + sin x)

Prove that (cos x + sin x)/(cos x - sin x) - (cos x - sin x)/(cos x + sin x) = 2 tan x

The number of distinct real roots of |(sinx, cosx, cosx),(cos x,sin x,cos x),(cos x,cos x,sin x)|=0 in the interval -(pi)/4 le x le (pi)/4 is

The number of distinct real roots of |(sinx, cosx, cosx),(cos x,sin x,cos x),(cos x,cos x,sin x)|=0 in the interval -(pi)/4 le x le (pi)/4 is

The number of distinct real roots of |(sinx, cosx, cosx),(cos x,sin x,cos x),(cos x,cos x,sin x)|=0 in the interval -(pi)/4 le x le (pi)/4 is