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Prove that tan^(-1).(1)/(sqrt2) + sin^(-...

Prove that `tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/(sqrt10) = -pi + cot^(-1) ((1 + sqrt2)/(1 - sqrt2))`

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`tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/(sqrt10)`
`= tan^(-1).(1)/(sqrt2) + tan^(-1).(1)/(2) - tan^(-1) 3`
`= tan^(-1).(1)/(sqrt2) -[tan^(-1) 3 - tan^(-1).(1)/(2)]`
`= tan^(-1).(1)/(sqrt2) - [tan^(-1).(3- (1)/(2))/(1 + (3)/(2))]`
`= tan^(-1).(1)/(sqrt2) - tan^(-1) 1`
`= tan^(-1).((1)/(sqrt2) -1)/(1 + (1)/(sqrt2))`
`= tan^(-1) (1 - sqrt2)/(1 + sqrt2)`
`= -pi + cot^(-1) ((1 + sqrt2)/(1 - sqrt2)) " " ( :' (1 - sqrt2)/(1 + sqrt2) lt 0)`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
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  2. If x gt y gt 0, then find the value of tan^(-1).(x)/(y) + tan^(-1) [(x...

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  3. Prove that tan^(-1).(1)/(sqrt2) + sin^(-1).(1)/(sqrt5) - cos^(-1).(1)/...

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  4. Solve : tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=pi/4

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  5. The number of real values of x satisfying tan^-1(x/(1-x^2))+tan^-1 (1...

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

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  7. Write the following function in the simplest form: tan^(-1)((3a^2x-x^3...

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  8. Solve the equation 2 tan^(-1) (cos x) = tan^(-1) (2 cosec x)

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  9. Solve the equations.tan^(-1)((1-x)/(1+x))=1/2tan^(-1)x ,(x >0)

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  10. If x + y + z = xyz and x, y, z gt 0, then find the value of tan^(-1) x...

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  11. If alpha and beta (alpha gt beta) are the roots of x^(2) + kx - 1 =0, ...

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  12. Find the sum cot^(-1) 2 + cot^(-1) 8 + cot^(-1) 18 + ...oo

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  13. Prove that sum(r=1)^(n) tan^(-1) ((2^(r -1))/(1 + 2^(2r -1))) = tan^(...

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  14. If cos^(-1).(x)/(2) + cos^(-1).(y)/(3) = (pi)/(6), then prove that (x^...

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  15. Prove that : cos^(-1) x + cos^(-1) ((x)/(2) + (sqrt( 3-3x^2) )/( 2) ) ...

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  16. solve the following equation sec^(-1).(x)/(a) - sec^(-1).(x)/(b) = sec...

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  17. If a^(2) + b^(2) = c^(2), c != 0, then find the non-zero solution of t...

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  18. If cos (theta - alpha) = a and sin(theta - beta) = b (0 lt theta - alp...

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  19. prove that, 2 tan^(-1) 2x = sin^(-1).(4x)/(1 + 4x^(2))

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  20. If x in (0, 1), then find the value of tan^(-1) ((1 -x^(2))/(2x)) + co...

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