`(cos(x/2)+sin(x/2))^2/(cos^2(x/2)-sin^2(x/2))`

lim_(xto(pi)) (1-sin(x/2))/(cos(x/2)(cos(x/4)-sin(x/4)))

Prove that (1+cos x)/(sin x) = (cos( x/2))/(sin (x/2))

2^(sin^(2)x)+2^(cos^(2)x) is

Let f(x)=|[cos(x+x^2),sin(x+x^2),-cos(x+x^2)],[sin(x-x^2),cos(x-x^2), sin(x-x^2)],[sin2x,0,sin(2x^2)]| . Find the value of f^(prime)(0) .

Number of solutions of equation 2"sin" x/2 cos^(2) x-2 "sin" x/2 sin^(2) x=cos^(2) x-sin^(2) x for x in [0, 4pi] is

int (cos^(2)x+sin 2x)/((2 cos x- sin x)^(2))dx

|(sin^(2) x,cos^(2) x,1),(cos^(2) x,sin^(2) x,1),(- 10,12,2)| =

(2+sin 2x)/(1+cos 2x) e^(x)

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).