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Prove each of the following tan^(-1) x...

Prove each of the following
`tan^(-1) x=-pi +cot^(-1) 1/x=sin^(-1) (x)/(sqrt(1+x^(2))`
`=-cos^(-1) (1)/(sqrt(1+x^(2))" when "x lt 0`

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MOTION-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise -3
  1. Find the value of cos^(-1){1/sqrt2(cos((9pi)/10)-sin((9pi)/10))}.

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  2. Find sin^(-1)(sintheta).cos^(-1)(costheta),tan^(-1)(tantheta),cot^(-1)...

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  3. Prove each of the following tan^(-1) x=-pi +cot^(-1) 1/x=sin^(-1) (x...

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  4. If -1<x<0,t h e ncos^(-1)x is equal to sec^(-1)1/x (b) pi-sin^(-1)sqr...

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  5. Find the value of tan[cos^(-1) (1/2) + tan^(-1) ( - 1/sqrt3)]

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  6. Sin[pi/3-sin^(-1)(-1/2)]

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  7. cos^(-1) ""(cos"" (7pi )/(6))

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  8. tan^(-1)("tan"(2pi)/3)

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  9. cos(tan^(-1)(3/4)) =

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  10. Simplify the following: tan("sin"^(-1)3/5+"cot"^(-1)3/2)

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  11. prove that , sin ^(-1) (cos) . sin ^(-1 )x+cos ^(-1)( sin) . cos ^...

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  12. Prove that 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x...

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  13. tan^(-1)((2mn)/(m^2-n^2))+tan^(-1)((2pq)/(p^2-q^2))=tan^(-1)((2MN)/(M^...

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  14. tan(tan^-1x+tan^-1y+tan^-1z)-cot(cot^-1x+cot^-1y+cot^-1z) is equal to

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  15. निम्नलिखित समीकरण को हल कीजिए - tan^(-1)((1-x)/(1+x))=(1)/(2)tan^(-1...

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  16. Prove that 3tan^-1(1/(2+sqrt3))-tan^-1(1/2)=tan^-1(1/3)

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  17. Find the number of values of x in [-pi/4, pi/4] satisfying the equatio...

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  18. Prove that cos^(-1) (sqrt(1/3))-cos^(-1) (sqrt((1)/(6)))+cos^(-1) ((...

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  19. Prove that 2 tan^(-1) (cosec tan^(-1) x - tan cot^(-1) x) = tan^(-1) x...

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  20. cos^(-1)((63)/(65))+2tan^(-1)((1)/(5))=sin^(-1)(3/5)

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