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Prove that: 3cos^(-1)x=cos^(-1)(4x^3-3x)...

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

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Let `cos^(-1)x=theta`
`RHS=cos^(-1)(4x^(3)-3x)`
`=cos^(-1)(4cos^(3)theta- 3 cos theta)`
`= cos^(-1)(cos 3 theta)`
`=3theta=3 cos^(-1)x` = LHS Hence Proved.
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NAGEEN PRAKASHAN ENGLISH-INVERES TRIGONOMETRIC FUNCTIONS-Exericse 2.2
  1. Prove that: 3sin^(-1)x=sin^(-1)(3x-4x^3), x in [-1/2,1/2]

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

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  3. Prove that : tan^(-1)2/(11)+tan^(-1)7/(24)=tan^(-1)1/2

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  4. Prove that: 2tan^(-1)1/2+tan^(-1)1/7=tan^(-1)(31)/(17)

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  5. Write the following function in the simplest form: tan^(-1)(sqrt(1+x^2...

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  6. tan^(- 1)(1/(sqrt(x^2-1))),|x|gt1

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  7. Express each of the following in the simplest form: tan^(-1){sqrt((...

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  8. tan^(-1)((cosx-sinx)/(cosx+sinx))=pi/4-x

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  9. tan^(-1)""(x)/(sqrt(a^(2)-x^(2))),|x|lt a

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  10. Write the following function in the simplest form: tan^(-1)((3a^2x-x^3...

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  11. For the principal values, evaluate each of the following: tan^(-1){2co...

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  12. Find the value of: cot(tan^(-1)a+cot^(-1)a)

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  13. Find the value of: tan1/2[sin^(-1)(2x)/(1+x^2)+cos^(-1)(1-y^2)/(1+y^2)...

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  14. If sin(sin^(-1)1/5+cos^(-1)x)=1, then find the value of xdot

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  15. tan^-1 (x-1)/(x-2) + tan^-1 (x+1)/(x+2)=pi/4. find X

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  16. Find the value of sin^(-1)(sin((2pi)/3))

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  17. Find the value of tan^(-1)(tan((3pi)/4))

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  18. Find the value of tan(sin^(-1)3/5+cot^(-1)3/2)

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  19. cos^(-1)(cos(7pi)/6)is equal to(a) (7pi)/6 (B) (5pi)/6 (C) pi/3 (D) pi...

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  20. sin(pi/3-sin^(-1)(-1/2))is equal to(A) 1/2 (B) 1/3 (C) 1/4 (D) 1

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