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Prove the following: 2tan^-1(frac{1}{3})...

Prove the following: `2tan^-1(frac{1}{3})+cos^-1(frac{3}{5}) = frac{pi}{2}`

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Prove the following: 2tan^-1(frac{1}{3}) = tan^-1(frac{3}{4})

Prove the following: 2tan^-1(frac{1}{3}) + tan^-1(frac{1}{7}) = frac{pi}{4}

Prove the following: cos^-1(frac{3}{5})+cos^-1(frac{4}{5}) = frac{pi}{2}

Prove the following: tan^-1(frac{1}{2})+tan^-1(frac{1}{3}) = frac{pi}{4}

Prove the following: 2tan^-1(frac{1}{2})+tan^-1(frac{1}{7}) = tan^-1(frac{31}{17})

Prove the following: sin^-1(frac{12}{13})+cos^-1(frac{4}{5})+tan^-1(frac{63}{16}) = pi

Prove the following: sin^-1(frac{1}{sqrt2})-3sin^-1(frac{sqrt3}{2}) = frac{-3pi}{4}

Prove the following: sin^-1(frac{3}{5})+cos^-1(frac{12}{13}) = sin^-1(frac{56}{65})

Prove the following: sin^-1(frac{8}{17})+sin^-1(frac{3}{5}) = sin^-1(frac{77}{85})

Prove the following: cos^-1(frac{4}{5})+cos^-1(frac{12}{13}) = cos^-1(frac{33}{65})

CHETANA PUBLICATION-Trignometric Functions-EXERCISE
  1. Find the value of the following:sin(sin^-1(frac{3}{5})+cos^-1(frac{3}{...

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  2. Find the value of the following: cos(cos^-1(-frac{1}{2})+tan^-1(sqrt3...

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  3. Prove the following: 2tan^-1(frac{1}{3})+cos^-1(frac{3}{5}) = frac{pi}...

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  4. Prove the following: 2tan^-1(frac{1}{3}) + tan^-1(frac{1}{7}) = frac{p...

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  5. Prove the following: tan^-1 1+tan^-1 2+tan^-1 3 = pi

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  6. Prove the following: cos^-1(frac{4}{5})+cos^-1(frac{12}{13}) = cos^-1(...

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  7. Prove the following: sin^-1(frac{8}{17})+sin^-1(frac{3}{5}) = sin^-1(...

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  8. Prove the following: tan^-1[frac{cosx+sinx}{cosx-sinx}] = frac{pi}{4}...

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  9. Prove the following: tan^-1[sqrt(frac{1-cosx}{1+cosx})] = frac{x}{2}

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  10. Prove the following: 2tan^-1(frac{1}{2})+tan^-1(frac{1}{7}) = tan^-1(...

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  11. Prove the following: tan^-1(frac{67}{19}) = tan^-1(frac{5}{13})+cos^-1...

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  12. Prove the following: sin^-1(frac{12}{13})+cos^-1(frac{4}{5})+tan^-1(...

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  13. Find the value of tan^-1(tan(frac{pi}{6}))

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  14. Find the value of sin^-1(sin(frac{3pi}{5}))

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  15. Simplify: tan^-1[frac{acosx-bsinx}{bcosx+asinx}] if frac{a}{b} tanx gt...

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  16. Find the value of the expression: tan^-1[sqrt(frac{1-cosx}{1+cosx})]

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  17. What is the range of sine inverse function?

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  18. What is the domain of cosine inverse function?

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  19. What is the domain of tan inverse function?

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  20. What is the range of secant inverse function?

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