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If "tan"^(-1)x+"tan"^(-1)y=(4pi)/(5), th...

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

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The correct Answer is:
`pi/(5)`
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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -CHAPTER PRACTICE
  1. Write the principal value of "cos"^(-1)("cos"(11pi)/(6)).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Directions (Q. Nos. 16-25) Prove the following "cos"["sin"^(-1)(3/(5...

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  17. Directions Prove the following "tan"^(-1)1/(4)+"tan"^(-1)2/(9)=1/(2)...

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  18. Directions Prove the following "tan"^(-1)((sqrt(1+"cos"x)+sqrt(1-"c...

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  19. Prove the following "tan"^(-1)((1-x)/(1+x))-"tan"^(-1)((1-y)/(1+y))=...

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  20. Directions (Q. Nos. 16-25) Prove the following "cos"(2"tan"^(-1)1/(7...

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