Prove the Statement:`"sin"^(-1)12/13-"sin"^(-1) 3/5 ="sin"^(-1) 33/65`

Prove statement "sin"^(-1) 3/5+ "sin"^(-1) 8/17="cos"^(-1) 36/85

Prove statement "sin"^(-1) 3/5+ "cos"^(-1)12/13="cos"^(-1) 33/65

Prove statement "sin"^(-1)4/5 +2"tan"^(-1) 1/3= pi/2

Prove statement "cos"^(-1) 12/13 +2"cos"^(-1) sqrt(64/65) +"cos"^(-1) sqrt(49/50) ="cos"^(-1)1/sqrt2

Prove statement "cos"" tan"^(-1) " cot sin"^(-1) x =x

Show that "sin"^(-1)(8/17)+"sin"^(-1)(3/5)="cos"^(-1)(36/85) .

Prove that: cos^(-1)(12/13)+sin^(-1)(3/5)=sin^(-1)(56/65)

Solve: "sin"^(-1)2x+"sin"^(-1)x = pi/3 .

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

Rectify the error if any in the following "sin"^(-1)4/(5)+"sin"^(-1)12/(13)+"sin"^(-1)33/(65) ="sin"^(-1)[4/(5)sqrt(1-44/(169))+12/(13)sqrt(1-16/(25))]+"sin"^(-1)33/(65) ="sin"^(-1)(56/(65))+"cos"^(-1)sqrt(1-(33/(65))^(2)) ="sin"^(-1)(56/(65))+"cos"^(-1)(56/(65))=pi/(2)