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Prove the following: tan^(-1)(1/7)+2\ ta...

Prove the following: `tan^(-1)(1/7)+2\ tan^(-1)(1/3)=pi/4`

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`tan^(-1)(1/7)+2\ tan^(-1)(1/3)`
`=tan^(-1)[frac{2/3}{1-(1/3)^2}]+tan^(-1)(1/7)`
`=tan^(-1)(frac{2/3}{8/9})+tan^(-1)(1/7)`
`=tan^(-1)(3/4)+tan^(-1)(1/7)`
`=tan^(-1)(25/25)`
`=pi/4`
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Prove the following: tan^(-1)(1/4)+tan^(-1)(2/9)=1/2cos^(-1)(3/5)=1/2s...

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  2. Prove: tan^(-1)(2/3)=1/2tan^(-1)(12/5)

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  3. Prove the following: tan^(-1)(1/7)+2\ tan^(-1)(1/3)=pi/4

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  4. Prove the following : sin^(-1)(4/5)+2\ tan^(-1)(1/3)=pi/2

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  5. Prove that 2sin^-1[3/5]-tan^-1[17/31]=pi/4

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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