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Find the values of each of the following...

Find the values of each of the following :
`sin(cos^(-1)sqrt3x+cos^(-1)x)=1` then find x.

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The correct Answer is:
`1/2`
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KUMAR PRAKASHAN-INVERSE TRIGONOMETRIC FUNCTIONS-PRACTICE WORK
  1. Find the values of each of the following : sin(pi/2-"cos"^(-1)3/7)+c...

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  2. Find the values of each of the following : tan^(-1)2x+tan^(-1)(1/(x+...

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  3. Find the values of each of the following : sin(cos^(-1)sqrt3x+cos^(-...

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  4. Find the values of each of the following : tan[sin^(-1)(3/5)+cos^(-1...

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  5. Find the value of sin^(-1)("cos"pi/8).

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  6. Find the value of tan^(-1)("tan"(5pi)/4).

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  7. Find the value of sin(2"tan"^(-1)4/3).

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  8. Find the value of sin[tan^(-1)("tan"(7pi)/6)]+cos[cos^(-1)("cos"(7pi...

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  9. If 4sin^(-1)x+cos^(-1)x=pi then find the value of x.

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  10. Find the value of the following : sin^(-1)(sin((7pi)/3))

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  11. Find the value of the following : cos^(-1)("cos"(5pi)/3)

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  12. Find the value of the following : cot^(-1)("cot"(7pi)/6)

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  13. Find the value of the following : sin^(-1)("sin"(3pi)/2)

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  14. Prove the following : 2"tan"^(-1)1/5+"tan"^(-1)1/4="tan"^(-1)32/43

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  15. Prove the following : "sin"^(-1)4/5+"sin"^(-1)5/13="cos"^(-1)16/65

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  16. Prove the following : tan^(-1)(1/3)+1/2("tan"^(-1)1/7)=pi/8

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  17. Prove the following : 2cot^(-1)(2)+cosec^(-1)(5/3)=pi/2

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  18. Prove the following : sin^(-1)(12/13)+cos^(-1)(4/5)+tan^(-1)(63/16)=...

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  19. Prove the following : 2sin^(-1)(5/13)=cos^(-1)(119/169)

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  20. Prove the following : "sin"^(-1)3/5+"cos"^(-1)4/5=cot^(-1)(7/24)

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