sin^(-1)((12)/(13))+cos^(-1)((4)/(5))+tan^(-1)((63)/(16))=pi

Let alpha=2tan^(-1)((1)/(2))+(sin^(-1)3)/(5) and beta=sin^(-1)((12)/(13))+cos^(-1)((4)/(5))+cos^(-1)((16)/(63)) be such that2sin alpha and cos beta are roots of the equation x^(2)-px+q=0, then (p-q) is

Prove that "sin"^(-1)(5)/(13) +"cos"^(-1)(3)/(5) ="tan"^(-1)(63)/(16) .

Column I, Column II sin^(-1)4/5+2tan^(-1)1/3= , p. pi/6 sin^(-1)(12)/(13)+cos^(-1)4/5+tan^(-1)(63)/(16)= , q. pi/2 If A=tan^(-1)(xsqrt(3))/(2lambda-x)a n dB=tan^(-1)((2x-lambda)/(lambdasqrt(3))) then the value of a-Bi s , r. pi/4 tan^(-1)1/7+2tan^(-1)1/3= , s. pi

Directions (Q. Nos. 16-25) Prove the following "sin"^(-1)(5/(13))+"cos"^(-1)(3/(5))="tan"^(-1)(63/(16)) .

Column I, Column II sin^(-1)(4/5)+2tan^(-1)(1/3)= , p. pi/6 ; sin^(-1)(12/13)+cos^(-1)(4/5)+tan^(-1)(63/16)= , q. pi/2 . If A=tan^(-1)((xsqrt(3))/(2lambda-x))a n d B=tan^(-1)((2x-lambda)/(lambdasqrt(3))) then the value of A-B is , r. pi/4 tan^(-1)1/7+2tan^(-1)1/3= , s. pi

Prove that cos^(-1)((3)/(5))+cos^(-1)((12)/(13))+cos^(-1)((63)/(65))=(pi)/(2)

Prove that sin^(-1)((4)/(5)) +sin^(-1)((5)/(13)) +sin^(-1)((16)/(65)) =(pi)/(2)

Prove that: sin^(-1)((4)/(5))+sin^(-1)((5)/(13))+sin^(-1)((16)/(65))=(pi)/(2)

Prove thate sin^(-1)((3)/(5))-cos^(-1)((12)/(13))=sin^(-1)((16)/(65))

Prove that, 2 "sin"^(-1)(2)/(sqrt(13))+(1)/(2) "cos"^(-1)(7)/(25)+"tan"^(-1)(63)/(16)=pi