MATHS HOLIDAY HOMEWORK:- Inverse Trigonometric Functions

Q.1. Find sin^-1(sin(3π/5)).

Q.2. Using principle value, evaluate                                                                                                                cos^-1(cos(2π/3))+sin^{- 1}(sin(2π/3))

Q.3. Evaluate sin^-1(sin(4π/5))

Q.4. Prove that sin^-1(4/5)+sin^-1(5/13)+sin^-1(16/65)=π/3

Q.5. Prove that Tan^-1(√x)=[cos^-1((1-x)/(1+x))]/2, where x€[0,1]

Q.6. Prove that 2Tan^-1(1/2)+Tan^-1(1/7)=Tan^-1(31/17)

Q.7. Prove that Tan^-1x+Tan^-1[2x/(1-x2)]=Tan^-1(3x-x3)/1-3x2]

Q.8. Prove that cos^-1x=sin^-1(1-x)/2)

Q.9. If Tan^-1a+Tan^-1b+Tan^-1c=π, Prove that a+b+c=abc