Solve `|sinx+cosx|=|sinx|+|cosx|,x in [0,2pi]dot`

Solve |sinx +cos x |=|sinx|+|cosx|, x in [0,2pi] .

Solve sinx +cosx =1

If m and n(n > m) are positive integers, then find the number of solutions of the equation n|sinx|=m|cosx|' for x in [0,2pi]dot Also find the solution.

Solve sinx-cosx +sqrt2=0 .

Solve: |-2x^2+1+e^x+sinx|=|2x^2-1|+e^x+|sinx|,x in [0,2pi]dot

The number of solution of 2cosx=|sinx| where x in [0.4pi] is/are

Separate the intervals of monotonocity for the function f(x)=sinx+cosx ,x in (0,2pi)

Find the value of x for which f(x)=sqrt(sinx-cosx) is defined, x in [0,2pi)dot

Discuss the extremum of f(x)=sinx(1+cosx),x in (0,pi/2)