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Solve the following equation: sin^(-1)x+...

Solve the following equation: `sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Solve sin^(-1)(1-x)-2sin ^(-1)x=pi/2

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  2. Solve: sin[2\ cos^(-1){cot(2\ tan^(-1)x)}]=0

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  3. Solve the following equation: sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x

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  4. Evaluateint(2x)/(1-x^2)\dx

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  5. If cos^-1 ((x^2-1)/(x^2+1))+ tan^-1 ((2x)/(x^2-1)) = (2pi)/3, then x e...

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  6. Evaluate int(5-x).x^2\dx

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  7. Evaluateint(2-x).x^3\dx

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

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

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

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

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

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

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

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

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

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

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

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

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

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