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What is the principal value of "cos"("...

What is the principal value of
`"cos"("cos"(2pi)/(3))+"sin"^(-1)("sin"(2pi)/(3))`?

Text Solution

Verified by Experts

The correct Answer is:
`pi`
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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -Part II (Sample Question )
  1. Evaluate each of the following "sin"^(-1)("sin"(2pi)/(3))

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  2. Evaluate each of the following "cos"^(-1)("cos"(7pi)/(6))

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  3. What is the principal value of "cos"("cos"(2pi)/(3))+"sin"^(-1)("sin...

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  4. Evaluate "cos"("tan"^(-1)3/(4))

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  5. Evaluate "sin"[pi/(3)-"sin"^(-1)(-1/(2))].

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  6. Evaluate "cos"["cos"^(-1)((-sqrt(3))/(2))+pi/(6)]

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  7. Simplify "cosec"("sin"^(-1)1/(5))+"sec"("cos"^(-1)1/(3)).

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  8. Evaluate "cot"("tan"^(-1)a+"cot"^(-1)a).

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  9. Evaluate "cos"(2"cos"^(-1)x+"sin"^(-1)x) at x=1/(5), where 0le"cos"^(-...

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

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  11. Evaluate "tan"("sin"^(-1)3/(5)+"cot"^(-1)3/(2)).

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  12. Write the value of "tan"(2"tan"^(-1)1/(5)).

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  13. Solve "sin"^(-1)(3/(5))+"sin"^(-1)(8/(17)).

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  14. Find the value of "cos"^(-1)((-7)/(25))+"cos"^(-1)(3/(5)).

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  15. Evaluate "sin"(3"sin"^(-1)0.4)

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  16. Find the value of "tan"1/(2)["sin"^(-1)(2x)/(1+x^(2))+"cos"^(-1)(1-y...

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  17. Show that "tan"^(-1)sqrt(x)=1/(2)"cos"^(-1)((1-x)/(1+x)),x in[0,1].

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  18. Write the simplest form of "sec"^(-1)(sqrt(1+x^(2))).

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  19. Express the expression in simplest form "cos"^(-1)((sqrt(4-x^(2)))/(2)...

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  20. Express the expression in simplest form "tan"^(-1)[x/(sqrt(a^(2)-x^(2)...

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