Solve the equations sin x + cos x =1

Solve the equation sin x + cos x -2sqrt2 sin x cos x =0

Find all the number 'a' for which any root of the equation sin 3x =a sin x +(4-2|a|)sin^(2) x is a root of the equation sin 3x + cos 2 x =1+2 sinx cos 2x and any root of the latter equation is a root of the former .

Solve the equation a cos x + cot x +1="cosec " x

Solve the equation ( cos x - sin x )(2 tan x +(1)/( cos x ))+2 =0

Solve the inequality . sin x cos x +(1)/(2) tan x ge 1

Find the number of solution of the equations sin^3 x cos x + sin^(2) x* cos^(2) x+sinx * cos^(3) x=1 , when x in[0,2pi]

Solve the equation (tan x )^( cos^(2) x)= ( cot x )^( sin x )

The solution of the equation : [sin x + cos x]^(1+sin2x)=2, -pi lexle pi , is :

Solve the following system of equations. sin x + cos y=1, cos 2x-cos 2y=1

Solve the equation sqrt3cos x + sin x = sqrt2 .