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

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

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Prove that : tan^(-1)(1/2) + tan^(-1)(1/3) = tan^(-1)(3/5) + tan^(-1)(1/4) = pi/4

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Prove the following: 2\ sin^(-1)(3/5)=tan^(-1)(24/7)

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  2. Prove the following: tan^(-1)(1/4)+tan^(-1)(2/9)=1/2cos^(-1)(3/5)=1/2s...

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

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

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

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

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  7. Prove the following: 2\ tan^(-1)(1/5)+tan^(-1)(1/8)= tan^(-1)(4/7)

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

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

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  10. Prove the following: 4\ tan^(-1)(1/5)-tan^(-1)(1/(239))=pi/4

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

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

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

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

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

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

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

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

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

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

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