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Find the values of the following: sin^...

Find the values of the following:
`sin^(-1)("sin"(4pi)/3)`

Text Solution

Verified by Experts

The correct Answer is:
`- (pi)/(3)`
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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-INVERSE TRIGONOMETRIC FUNCTIONS-SOLVED PROBLEMS
  1. Evaluate the following. sec^(-1) (-sqrt2)

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  2. Find the values of the following: cosec^(-1)(2/(sqrt(3)))

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  3. Find the values of the following: sin^(-1)("sin"(4pi)/3)

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  4. Find the values of the following: cos^(-1)("cos"(4pi)/3)

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  5. Find the values of the following: tan^(-1)("tan"(4pi)/3)

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  6. Find the values of the following: sin("cos"^(-1)5/13)

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  7. Find the values of the following: tan("Sec"^(-1)25/7)

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  8. Find the values of the following cos("tan"^(-1)24/7)

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  9. Find the values of the following: sin^(2)("Tan"^(-1)3/4)

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  10. Find the values of the following: sin((pi)/2-Sin^(-1)(-4/5))

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  11. Find the value of the following: cos(Cos^(-1)(-2/3)-Sin^(-1)(2/3))

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  12. Show that Sec^(2)(cot^(-1)3)+(Cosec^(2)(tan^(-1)2))=85/36

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  13. Find the value of the following cot^(-1)(1/2)+cot^(-1)(1/3)

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  14. Prove that Sin^(-1)(4/5)+Sin^(-1) 7/25 = Sin^(-1) 117/125.

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  15. If x in (-1,1) prove that 2Tan^(-1)x="Tan"^(-1)(2x)/(1-x^(2))

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  16. sin^(-1)(4/5)+sin^(-1)(5/13)+sin^(-1)(16/65)=

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  17. Prove that Cot^(-1)9+"Cosec"^(-1) (sqrt(41))/4 = (pi)/4.

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  18. Show that cot(Sin^-1sqrt(13/17))=sin(Tan^-1""2/3).

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  19. Find the value of tan(2"Tan"^(-1)(1/5)-(pi)/4)

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  20. Prove that sin^(-1)((4)/(5))+2 Tan^(-1)((1)/(3)) = (pi)/2.

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