Let `f(x)=sin^3x+lambdasin^2x ,-pi/2

Let f(x)=-sin^3x+3sin^2x+5 on [0,pi/2] . Find the local maximum and local minimum of f(x)dot

Separate the intervals of monotonocity of the function: f(x)=-sin^3x+3sin^2x+5,x in [-pi/2,pi/2]dot

Let f(x)=sin^(2)(x +alpha)+sin^(2)(x +beta)-2cos(alpha-beta)sin(x+alpha)sin(x +beta) . Which of the following is TRUE ?

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)| , then the value of int_0^(pi//2){f(x) + f'(x)} dx is

Match the column Column I (Function), Column II (Period) p. f(x)=sin^3x+cos^4x , a. pi/2 q. f(x)=cos^4x+sin^4x , b. pi r. f(x)=sin^3x+cos^3x , c. 2pi s. f(x)=cos^4x-sin^4x ,

Let f(x)=|[1+sin ^2 x, cos ^2 x , 4 sin 2 x],[ sin ^2 x ,1+cos ^2 x , 4 sin 2 x],[ sin ^2 x , cos ^2 x , 1+4 sin 2 x]| , the maximum value of f(x) is

Let f(x)=|2cos^2xsin2x-sinxsin2x2sin^2xcosxsinx-cosx0| . Then the value of int_0^(pi//2)[f(x)+f^(prime)(x)]dx is a. pi b. pi//2 c. 2pi d. 3pi//2

Statement 1: Let f(x)=sin(cos x)in[0,pi/2]dot Then f(x) is decreasing in [0,pi/2] Statement 2: cosx is a decreasing function AAx in [0,pi/2]

If f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4)=1, then (gof)(x) is ____________

If f(x)=sin^2x+sin^2(x+pi/3)+cosxcos(x+pi/3)a n dg(5/4=1, then (gof)(x) is ____________