" 51."(x^(2)+2)/(sqrt(cos x))

The value of int_(0)^( pi/2)(sqrt(cos x))/(sqrt(sin x)+sqrt(cos x))dx

If tanx=b/a then sqrt((a+b)/(a-b))+sqrt((a-b)/(a+b))= ........................... A) (2 sin x)/(sqrt(sin2x)) B) (2 cos x)/(sqrt(cos2x)) C) (2 cos x)/(sqrt(sin2x)) D) (2 sin x)/(sqrt(cos2x))

If I=int(sin x+sin^(3)x)/(cos2x)dx=P cos x+Q log|f(x)|+R then (a)P=(1)/(2),Q=-(3)/(4sqrt(2))(b)P=(1)/(4),Q=(1)/(sqrt(2)) (c) f(x)=(sqrt(2)cos x+1)/(sqrt(2)cos x-1)(d)f(x)=(sqrt(2)cos x-1)/(sqrt(2)cos x+1)

The value of lim_(x rarr0)(1)/(x^(2))sqrt((1-cos2x)/(1+cos2x))sqrt((1-cos x)/(1+cos x)) is equal to

If x in (pi, 2pi) , prove that ((sqrt(1+cosx))+(sqrt(1-cos x)))/((sqrt(1+cos x)) -sqrt(1-cos x)) = cot(pi/4 +x/2)

If pi

f(x)=sqrt(sin(cos x))+ln(-2cos^(2)x+3cos x+1)+e^(cos^(-1))((2sin x+1)/(2sqrt(2sin x)))

tan ^(-1) ""{(sqrt(1+cos x)+sqrt(1-cos x)}/{sqrt(1+cosx)-sqrt(1-cos x)}}=(pi)/(4)+(x)/(2) , 0 lt x lt (pi)/(2)

If int(cos ec^(2)x)ln(cos x+sqrt(cos2x))dx=f(x)ln(cos x+sqrt(cos2x))+g(x)+f(x)-x+ then f^(2)(x)-g^(2)(x) is equal to