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Prove that: 2tan^(-1)(1/2)+tan^(-1)(1/7...

Prove that: `2tan^(-1)(1/2)+tan^(-1)(1/7)=tan^(-1)((31)/(17))`

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`2tan^(-1)(1/2)+tan^(-1) (1/7)`
`=tan^(-1)(frac{2. 1/2}{1-(1/2)^2})+tan^(-1) (1/7)`
`=tan^(-1) (1/frac{3}{4})+tan^(-1) (1/7)`
`=tan^(-1) (4/3)+tan^(-1) (1/7)`
`=tan^(-1)(frac{frac{28+3}{21}}{frac{21-4}{21}])`
`=tan^(-1) (31/17)`
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Prove that 2sin^-1[3/5]-tan^-1[17/31]=pi/4

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  2. Prove the following: 2\ tan^(-1)(3/4)-tan^(-1)((17)/(31))=tan^(-1)(pi/...

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  3. Prove that: 2tan^(-1)(1/2)+tan^(-1)(1/7)=tan^(-1)((31)/(17))

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  4. Prove that: tan^(-1)((1-x^2)/(2x))+cot^(-1)((1-x^2)/(2x))pi/2

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  5. Prove that: sin{tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2))}=1

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  6. If sin^(-1) ((2a)/(1+a^2))+ sin^(-1) ((2b)/(1+b^2)) = 2 tan^(-1)x then...

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  7. Show that :2tan^(-1)x+sin^(-1)((2x)/(1+x^2)) is constant for xgeq1, fi...

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  8. Find the value of: tan^(-1)[2cos(2sin^(-1)(1/2))]

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  9. Find the value of cos(sec^(-1)x+"c o s e c"^(-1)x) , |x|geq1

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  10. Find the value of tan^(-1)((x-2)/(x-1))+tan^(-1)((x+2)/(x+1))=pi/4

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  11. Solve the following equation for x:tan^(-1)(1/4)+2tan^(-1)(1/5)+tan^(-...

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  12. Solve 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x...

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  13. Solve the following equation for x: tan^(-1)((2x)/(1-x^2))+cot^(-1)...

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  14. Solve for x : 2tan^(-1)(sinx)=tan^(-1)(2secx),\ x!=pi/2

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  15. Solve for x : cos^(-1)((x^2-1)/(x^2+1))+1/2tan^(-1)((2x)/(1-x^2))=(2pi...

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  16. prove that 2tan^-1(sqrt((a-b)/(a+b))tan(theta/2))=cos^-1((acostheta+b)...

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  17. Show that (tan^-1)(2ab)/(a^2-b^2)+(tan^-1)(2xy)/(x^2-y^2)=(tan^-1) (2a...

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  18. For any a ,\ b ,\ x ,\ y >0 , prove that : 2/3tan^(-1)((3a b^2-a^3)/(b...

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  19. Write the value of sin^(-1)(-(sqrt(3))/2)+cos^(-1)(-1/2) .

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  20. Write the difference between maximum and minimum values of sin^(-1)...

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