Show that `0le3sin sqrt(pi^2/16-x^2) le 3/sqrt(2)`

Solve sqrt(x-2) le 3

Prove that 4le int_(1)^(3) sqrt(3+x^(3)) dx le 2sqrt30 .

Show that "sin"^(-1)(sqrt(3))/2+"tan"^(-1)1/(sqrt(3))=(2pi)/3

The number of real solution of the equation sqrt(1 + cos 2x) = sqrt2 sin^(-1) (sin x), -pi le x le pi , is

The number of real solution of the equation sqrt(1 + cos 2x) = sqrt2 sin^(-1) (sin x), -pi le x le pi , is

Prove the following inequalities : (i) (sqrt(3))/(8) lt int_(pi//4)^(pi//3)(sinx)/(x)dx lt (sqrt(2))/6 , (ii) 4 le int_(1)^(3)sqrt((3x^(2)+x^(2)))dx le 20 sqrt(30)

The number of distinct real roots of the equation sqrt(sin x)-(1)/(sqrt(sin x))=cos x("where" 0le x le 2pi) is

If 0 le x le 2pi , then 2^(cosec^(2) x) sqrt(1/2 y^(2) -y+1) le sqrt(2)

If (1)/sqrt(2) le x le 1 then sin^(-1) 2xsqrt(1-x^(2)) equals

Consider the function f(theta)=int_(0)^(1)(|sqrt(1-x^(2))-sintheta|)/(sqrt(1-x^(2)))dx , where 0le theta le (pi)/2 , then