Home
Class 12
MATHS
Prove that: i) sin^(-1)(3x-4x^(3))=3si...

Prove that:
i) `sin^(-1)(3x-4x^(3))=3sin^(-1)x, |x| le 1/2`
ii) `cos^(-1)(4x^(2)-3x)=3cos^(-1)x,1/2 le x le 1`
iii) `tan^(-1)""(3x-x^(3))/(1-3x^(2))=3tan^(-1)x, |x| lt 1/sqrt(3)`
iv) `tan^(-1)x+tan^(-1)""(2x)/(1-x^(2))=tan^(-1)""(3x-x^(3))/(1-3x^(2))`

Text Solution

Verified by Experts

i) Put `x=sintheta`, ii) Put `x=costheta`, iii) Put `x=tantheta`, iv) Use `tan^(-1)A+tan^(-1)B`
Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Exercise 4D|6 Videos

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Objective Questons|57 Videos

  • INVERSE TRIGNOMETRIC FUNCTIONS

    RS AGGARWAL|Exercise Exercise 4B|22 Videos

  • INTEGRATION USING PARTIAL FRACTIONS

    RS AGGARWAL|Exercise Objective Questions Ii|37 Videos

  • LINEAR DIFFERENTIAL EQUATIONS

    RS AGGARWAL|Exercise Objective Questions|27 Videos

Similar Questions

Explore conceptually related problems

tan^(-1)x+tan^(-1)(2x)/(1-x^(2))=pi+tan^(-1)(3x-x^(3))/(1-3x^(2)),(x>0)

Prove that sin^(-1)(3x-4x^3)=3sin^(-1)x,x in[1/2,1]

Prove the following: tan^(-1)x+tan^(-1)((2x)/(1-x^(2)))=tan^(-1)((3x-x^(3))/(1-3x^(2)))

tan^(-1)x+(tan^(-1)(2x))/(1-x^(2))=tan^(-1)((3x-x^(3))/(1-3x^(2))),|x|<(1)/(sqrt(3))

Prove that cos^(-1)(3x-4x^3)=3cos^(-1)x,x in[1/2,1]

tan^(-1)2x+tan^(-1)3x=(pi)/(4)

Differentiate tan^(-1)((3x-x^(3))/(1-3x^(2))), if x>(1)/(sqrt(3))

Differentiate tan^(-1)((3x-x^(3))/(1-3x^(2))), if -1/(sqrt(3))

Differentiate tan^(-1)((3x-x^(3))/(1-3x^(2))), if x<-(1)/(sqrt(3))

Define: tan^(-1)((3x-x^(3))/(1-3x^(2))) in terms of tan^(-1)x