(37sqrt(pi))/(1+x^(2))

If f(x)=sqrt(1+cos^(2)(x^(2))), then f'((sqrt(pi))/(2)) is (sqrt(pi))/(6)(b)-sqrt(pi/6)1/sqrt(6)(d)pi/sqrt(6)

Let g(x)=sqrt(sin^(-1)(cos(tan^(-1)x))+cos^(-1)(sin(cot^(-1)x))) ,then int_(-sqrt((pi)/(2)))^(sqrt((pi)/(2)))g(x)dx equals

Evalute lim_ (x rarr (pi) / (2)) (sqrt (2-sin x) -1) / (((pi) / (2) -x) ^ (2))

If cos (pi/12) = (sqrt(2) + sqrt(6))/(4) , then all x in (0,pi/2) such that (sqrt(3)-1)/(sin x) + (sqrt(3)+1)/(cos x) = 4sqrt(2) , then find x.

If cos (pi/12) = (sqrt(2) + sqrt(6))/(4) , then all x in (0,pi/2) such that (sqrt(3)-1)/(sin x) + (sqrt(3)+1)/(cos x) = 4sqrt(2) , then find x.

solve : tan^(-1) sqrt(x(x+1))+sin ^(-1) (sqrt(1+x+x^(2)))=(pi)/(2)

If sin^(-1)x+sin^(-1)y=(pi)/(2) and sin2x=cos2y, then (a)x=(pi)/(8)+sqrt((1)/(2)-(pi^(2))/(64))(b)y=sqrt((1)/(2)-(pi^(2))/(64))-(pi)/(12)(c)x=(pi)/(12)+sqrt((1)/(2)-(pi^(2))/(64))(d)y=sqrt((1)/(2)-(pi^(2))/(64))-(pi)/(8)

Prove that tan^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=(pi)/(4)+(1)/(2) cos^(-1)x^(2) .

Show that : tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))]=pi/4+1/2cos^(-1)x^(2) .

tan^(-1)[(sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2)))]=(pi)/(4)+(1)/(2)cos^(-1)x^(2)