1.`sin(x^(2)+5) ` 2. `cos(sin x)`

If the maximum and minimum values of the determinant |(1 + sin^(2)x,cos^(2) x,sin 2x),(sin^(2) x,1 + cos^(2) x,sin 2x),(sin^(2) x,cos^(2) x,1 + sin 2x)| are alpha and beta , then

"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).

Solve 2 sin^(2) x-5 sin x cos x -8 cos^(2) x=-2 .

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

General solution of sin^(2) x-5 sin x cos x -6 cos^(2)x=0 is

Solve (sin^(2) 2x+4 sin^(4) x-4 sin^(2) x cos^(2) x)/(4-sin^(2) 2x-4 sin^(2) x)=1/9 .

The number of solution of the equation sin^(3)x cos x+sin^(2)x cos^(2)x+cos^(3)x sin x=1 in the interval [0, 2pi] is equal to

(i) int(cos^(3) x+ sin^(3) x)/(sin^(2) x.cos ^(2) x)dx " "(ii) int(cos2x)/(cos^(2) x sin^(2)x) dx

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