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Prove that: (alpha^3)/2cos e c^2(1/2tan^...

Prove that: `(alpha^3)/2cos e c^2(1/2tan^(-1)(alpha/beta))+(beta^3)/2s e c^2(1/2tan^(-1)(beta/alpha))=(alpha+beta)(alpha^2+beta^2)` .

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Evaluateint(2-x).x^3\dx

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  2. Show taht 2tan^-1(tan(alpha/2)tan(pi/4-beta/2))=tan^-1((sinalphacosbet...

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  3. Prove that: (alpha^3)/2cos e c^2(1/2tan^(-1)(alpha/beta))+(beta^3)/2s ...

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  4. Prove that : tan^(-1){(cos2\ alphasec2\ beta+cos2betasec2alpha)/2}=tan...

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  5. Evaluate the following: (i) tan{2\ tan^(-1)(1/5)-pi/4} (ii) tan(1/2...

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  6. Evaluate the following:(i) sin(1/2\ cos^(-1)(4/5)) (ii) sin(2\ tan^...

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  7. Prove the following: 2\ sin^(-1)(3/5)=tan^(-1)(24/7)

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

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

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

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

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

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

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

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

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

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

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

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

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

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