If ` sin x +cos x =1`, then x =

Solve |cos x - 2 sin 2x - cos 3 x|=1-2 sin x - cos 2x .

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

Solve the equation ( sin x + cos x )^(1+ sin 2x )=2 , when -pi le x le pi .

alpha is a root of equation ( 2 sin x - cos x ) (1+ cos x)=sin^2 x , beta is a root of the equation 3 cos ^2x - 10 cos x +3 =0 and gamma is a root of the equation 1-sin2 x = cos x- sin x : 0 le alpha , beta, gamma , le pi//2 sin alpha + sin beta + sin gamma can be equal to

alpha is a root of equation ( 2 sin x - cos x ) (1+ cos x)=sin^2 x , beta is a root of the equation 3 cos 2x - 10 cos x +3 =0 and gamma is a root of the equation 1-sin2 x = cos x- sin x : 0 le alpha , beta, gamma , le pi//2 cos alpha + cos beta + cos gamma can be equal to

alpha is a root of equation ( 2 sin x - cos x ) (1+ cos x)=sin^2 x , beta is a root of the equation 3 cos 2x - 10 cos x +3 =0 and gamma is a root of the equation 1-sin2 x = cos x- sin x : 0 le alpha , beta, gamma , le pi//2 sin (alpha - beta ) is equal to

Statement -1: If 2"sin"2x - "cos" 2x=1, x ne (2n+1) (pi)/(2), n in Z, "then sin" 2x + "cos" 2x = 5 Statement-2: "sin"2x + "cos"2x = (1+2"tan" x - "tan"^(2)x)/(1+"tan"^(2)x)

int_(0)^(pi//2) ( sin x cos x )/( 1+ sin x ) dx is equal to

If f (x) = sqrt(cos ec ^(2) x - 2 sin x cos x - (1)/(tan ^(2) x )) x in ((7pi)/(4), 2pi ) then f' ((11 pi)/(6))=

Let f(x) = sin x (1+cos x) , x in (0,2pi). Find the number of critical points of f(x) . Also identify which of these critical points are points of Maxima // Minima.