Show that: `sin(pi/2 - x)` = cos x`

Show that cos((pi)/(2)-x)=sin x

If "sin" x + "sin"^(2) x = 1 show that: cos^(4)x + cos^(2)x = 1 (ii) If "sin" x + cos x =sqrt(2) cos x show that: sqrt2 sin x = cos x - sin x

Show that 2x>3sin x-x cos x,0

Show that: int_(0)^( pi/2)f(sin2x)sin xdx=sqrt(2)int_(0)^( pi/4)f(cos2x)cos xdx

Prove that : int_(0)^(pi//2) (x sin x cos x)/(sin^(4) x+ cos^(4)x)dx =(pi)/(16)

Show that f(x)=tan^(-1)(sin x+cos x) is decreasing function on the interval ((pi)/(4),(pi)/(2))

Show that f(x)=tan^(-1)(sin x+cos x) is a decreasing function on the interval on (pi/4,pi/2).

Show that f(x)=sin x(1+cos x) is maximum at x=(pi)/(3) in the interval [0,pi] .

Show that f(x)=sin x(1+cos x) is maximum at x=(pi)/(3) in the interval [0,pi]