" If "2cos y=x+(1)/(x)," prove that "cos2y=(1)/(2)(x^(2)+(1)/(x^(2)))

2cos y=x+(1)/(x), provethat cos2y=(1)/(2)(x^(2)+(1)/(x^(2)))

Prove that cos^(-1){(1+x)/(2)}=(cos^(-1)x)/(2)

If y=(cos^(-1)x)^(2) prove that (1-x^(2))(d^(2)y)/(dx^(2))-x(dy)/(dx)-2=0

If sin(x+y)=y cos(x+y) ,then prove that (dy)/(dx)=-(1+y^(2))/(y^(2))

Prove that cos^(-1){(1+x)/2}=(cos^(-1)x)/2

If y = "cos"^(-1) ((3 + 5 cos x)/(5 + 3 cos x)) , prove that cos x = 2 tan^(-1) (1/2 tan (x/2) )

Ify,=sqrt(((1+cos x)/(2))), provethat (dy)/(dx)=-(1)/(2)(sin x)/(2) If y,=sqrt((1+sin x)/(1-sin x)), prove that cos x(dy)/(dx)=y

If y=tan^(-1)sqrt((1-cos x)/(1+cos x)), prove that (dy)/(dx)=(1)/(2)

If y=cot^(-1)(sqrt(cos x))-tan^(-1)(sqrt(cos x)), prove that sin y=tan^(2)(x)/(2)