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cot^(-1)((1+cosx)/(sinx))...

`cot^(-1)((1+cosx)/(sinx))`

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Derivative fo tan^(-1)((sinx)/(1+cosx))w.r.t.tan^(-1)((cosx)/(1+sinx)) is

intcot^(-1)((1+sinx)/(cosx))dx=

cosx+sinx=1

tan^-1(cosx/(1-sinx))

cot^(-1)((cosx-sinx)/(cosx+sinx))

int tan^(-1)[(cosx)/(1-sinx)]dx=

Express each of the following in the simplest form: tan^(-1){(cosx)/(1-sinx)},\ -pi/2

Find the value of int_(0)^(pi)(cot^(-1)(sinx-(1)/(2))+cot^(-1)((2)/(2sinx-1)))dx .

(d)/(dx)((cosx)/(1+sinx))=

Prove that : tan^(-1)((cosx)/(1-sinx))-cot^(-1)(sqrt((1+cosx)/(1-cosx)))=(pi)/(4), x in (0, pi//2) .

MODERN PUBLICATION-CONTINUITY AND DIFFERENTIABILITY-EXERCISE 5(e) (SHORT ANSWER TYPE QUESTIONS)
  1. Differentiate the following w.r.t. x : xsec^(-1)x.

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  2. Differentiate the following w.r.t. x : cos^(-1)(sinx)

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  3. Differentiate the following w.r.t. x: (i)sin^(-1)2x" "(ii)tan^(-...

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  4. Differentiate the following w.r.t. x : (cot^(-1)x)^(2)

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  5. Differentiate the following w.r.t. x : sin(2sin^(-1)x)

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  6. Find the derivatives w.r.t. x : tan^(-1)((sinx)/(1+cosx))

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  7. "Tan"^(-1)(cosx)/(1+sinx)=

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  8. cot^(-1)((1+cosx)/(sinx))

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  9. Differentiate the following w.r.t. x : sin^(-1)(1-2x^(2))

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  10. sin^(-1)(3x-4x^(3))

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  11. Differentiate the following w.r.t. x : cos^(-1)(4x^(3)-3x),-1ltxlt1

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  12. Differentiate the following w.r.t. x : sin^(-1)((2x)/(1+x^(2))),-1lt...

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  13. "cosec"^(-1)((1+x^(2))/(2x))

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  14. Differentiate the following w.r.t. x : sin^(-1)((1-x^(2))/(1+x^(2)))...

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  15. Differentiate the following w.r.t. x : cos^(-1)((1-x^(2))/(1+x^(2)))...

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  16. Differentiate the following w.r.t. x : cos^(-1)((2x)/(1+x^(2))),-1lt...

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  17. Differentiate the following w.r.t. x : tan^(-1)((2x)/(1-x^(2))),0ltx...

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  18. tan^(-1)((3x-x^(3))/(1-3x^(2)))

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  19. निम्न फलन का x के सापेक्ष अवकल गुणांक ज्ञात कीजिए - tan ^(-1) [(x^(1/...

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  20. "tan"^(-1)(x)/(sqrt(a^(2)-x^(2)))

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