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Prove that xy<1, tan^-1x+tan^-1y=tan^-...

Prove that `xy<1`,
`tan^-1x+tan^-1y=tan^-1(frac(x+y)(1-xy))`

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Prove that 2 sin^-1(frac(3)(5))=tan^-1(frac(24)(7))

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Using the above result prove that tan^-1(frac(1)(2))+tan^-1(frac(1)(3))=pi/4

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MAXIMUM PUBLICATION-INVERSE TRIGNOMETRY-EXAMPLE
  1. show that sin^-1frac(3)(5)-sin^-1frac(8)(17)=cos^-1frac(84)(85)

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  2. Choose the correct answer from the bracket. if cos^-1x=y,then y is...

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  3. find the value of cos^-1cos((7pi)/3)

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  4. Solve for x if,tan^-1(frac(1+x)(1-x))=2tan^-1x

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  5. Find the principal value of cos^-1(frac(sqrt3)(2))

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  6. Prove that 2 sin^-1(frac(3)(5))=tan^-1(frac(24)(7))

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  7. Prove 2tan^-1frac(1)(2)+tan^-1frac(1)(7)=tan^-1frac(31)(17)

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  8. Find the principal value of cos^-1(-frac(1)(2))

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  9. Show that tan^-1(frac(cosx)(1-sinx))=pi/4+x/2

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  10. The principal value of cos^-1(-frac(1)(2))

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  11. Express tan^-1(frac(cosx)(1-sinx)) in the simplest Form.

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  12. Write the principal value of sin^-1(frac(1)(2))

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  13. show that sin^-1(frac(3)(5))-sin^-1(frac(8)(17))=cos^-1(frac(84)(85)...

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  14. The principal value of tan^-1(-1) is [pi/4,-pi/4,pi-pi/4,pi+pi/4]

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  15. If tan^-1(frac(x-1)(x-2))+tan^-1(frac(x+1)(x+2))=pi/4, then find the...

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  16. Give an expression for tan(x+y)

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  17. Prove that xy<1, tan^-1x+tan^-1y=tan^-1(frac(x+y)(1-xy))

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  18. Using the above result prove that tan^-1(frac(1)(2))+tan^-1(frac(1)(...

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  19. Show that tan^-1frac(1)(5)+tan^-1frac(1)(7)+tan^-1frac(1)(3)+tan^-1f...

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  20. Given that cot3theta=frac(3cot^2theta-1)(cot^3theta-3cottheta),show ...

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