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Evaluate "cos"^(-1)(1/(2))+2"sin"^(-1)(1...

Evaluate `"cos"^(-1)(1/(2))+2"sin"^(-1)(1/(2))`.

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The correct Answer is:
`(2pi)/(3)`
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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -CHAPTER PRACTICE
  1. Evaluate "cos"^(-1)(1/(2))+2"sin"^(-1)(1/(2)).

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  2. Evaluate "cot"^(-1)(-sqrt(3)).

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  3. Evaluate tan^(-1)(1)+cos^(-1)((-1)/(2)).

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  4. Write the value of "sin"^(-1)("sin"1550^(@)).

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  5. Write the value of "tan"^(-1)["tan"((15pi)/(4))].

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  6. Find the domain of the function "cos"^(-1)(2x-1).

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  7. Write the principal value of "cos"^(-1)("cos"(11pi)/(6)).

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  8. Find the principal value of "tan"^(-1)("tan"(7pi)/(6)).

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  9. If "tan"^(-1)x+"tan"^(-1)y=(4pi)/(5), then find "cot"^(-1)x+"cot"^(-1)...

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  10. If "tan"^(-1)(sqrt(3))+"cot"^(-1)x=pi/(2), then find x.

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  11. If "tan"^(-1)x+"tan"^(-1)y=pi/4,xylt1, then write the value of x+y+x...

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  12. Simplify 2"tan"^(-1)x+"sin"^(-1)((2x)/(1+x^(2))) in terms of "tan"^(-1...

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  13. Find the value of "cos"^(-1)("cos"(5pi)/(3))+"sin"^(-1)("sin"(5pi)/(3)...

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  14. Find the value of 2"sec"^(-1)2+"sin"^(-1)(1/(2)).

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  15. Solve for x, "sin"^(-1)((2alpha)/(1+alpha^(2)))+"sin"^(-1)((2beta)/(...

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  16. Show that "sin"^(-1)(2xsqrt(1-x^(2)))=2"sin"^(-1)x.

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  17. Directions (Q. Nos. 16-25) Prove the following "cos"^(-1)x="tan"^(-1...

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  18. Directions (Q. Nos. 16-25) Prove the following 2"tan"^(1)1/(2)+"tan"...

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  19. Prove that tan^(-1)((1)/(5)) +tan^(-1)((1)/(7)) +tan^(-1)((1)/(3)) +...

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  20. Directions (Q. Nos. 16-25) Prove the following "sin"^(-1)(5/(13))+"c...

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  21. Directions (Q. Nos. 16-25) Prove the following "cos"["tan"^(-1){"sin...

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