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Prove the followings : cot^(-1)((sqrt(...

Prove the followings :
`cot^(-1)((sqrt(1+x^(2))-1)/x)=pi/2-1/2tan^(-1)x`

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Prove the following : tan^(-1)(1/3)+1/2("tan"^(-1)1/7)=pi/8

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Prove the followings : If tan^(-1)((yz)/(xr))+tan^(-1)((zx)/(yr))+tan^(-1)((xy)/(zr))=pi/2 then x^(2)+y^(2)+z^(2)=r^(2) .

Prove the followings : cos^(-1)x=2sin^(-1)sqrt((1-x)/2)=2cos^(-1)sqrt((1+x)/2)

Solve the following equations : tan^(-1)(2x)+tan^(-1)(3x)=pi/4

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KUMAR PRAKASHAN-INVERSE TRIGONOMETRIC FUNCTIONS-PRACTICE WORK
  1. Prove the following : tan^(-1)(1/3)+1/2("tan"^(-1)1/7)=pi/8

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  2. Prove the following : 2cot^(-1)(2)+cosec^(-1)(5/3)=pi/2

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  3. Prove the following : sin^(-1)(12/13)+cos^(-1)(4/5)+tan^(-1)(63/16)=...

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  4. Prove the following : 2sin^(-1)(5/13)=cos^(-1)(119/169)

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  5. Prove the following : "sin"^(-1)3/5+"cos"^(-1)4/5=cot^(-1)(7/24)

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  6. Prove the followings : "cot"^(-1)(ab+1)/(a-b)+"cot"^(-1)(bc+1)/(b-c)...

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  7. Prove the followings : If cos^(-1)a+cos^(-1)b+cos^(-1)c=pi then a^(2...

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  8. Prove the followings : If tan^(-1)x+tan^(-1)y+tan^(-1)z=pi then x+y+...

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  9. Prove the followings : If "cos"^(-1)x/2+"cos"^(-1)y/3=theta then 9x^...

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  10. about to only mathematics

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  11. Prove the followings : cot^(-1)((sqrt(1+x^(2))-1)/x)=pi/2-1/2tan^(-1...

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  12. Prove the followings : If tan^(-1)((yz)/(xr))+tan^(-1)((zx)/(yr))+ta...

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  13. Prove the followings : If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi then xsqr...

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  14. Prove the followings : If 0ltxlt1andtan^(-1)(1-x),tan^(-1)xandtan^(-...

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  15. Prove the followings : tan(pi/4+1/2"cos"^(-1)a/b)+tan(pi/4-1/2"cos"^...

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  16. Solve the following equations : tan^(-1)(2x)+tan^(-1)(3x)=pi/4

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  17. Solve the following equations : tan^(-1)(1)+cos^(-1)(1/sqrt2)=sin^(-...

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  18. Solve the following equations : sin^(-1)(5/x)+sin^(-1)(12/x)=pi/2

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  19. Solve the following equations : sin^(-1)x+cos^(-1)(2x)=pi/6

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  20. Solve the following equations : cos^(-1)(sqrt3x)+cos^(-1)x=pi/2

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