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Write the following functions in the sim...

Write the following functions in the simplest form: `tan^(-1){x/(sqrt(a^2-x^2))}`

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`tan ^{-1} frac{x}{sqrt{a^{2}-x^{2}}}`
` Let x=a sin theta`
` frac{x}{a}=sin theta Rightarrow theta=sin ^{-1} frac{x}{a}`
Therefore,
` =tan ^{-1} frac{x}{sqrt{a^{2}-x^{2}}}`
` ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Prove that: tan^(-1)((1-x^2)/(2x))+cot^(-1)((1-x^2)/(2x))=pi/2

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  2. Simplify each of the following: cos^(-1)(3/5cosx+4/5sinx) , where -(...

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  3. Write the following functions in the simplest form: tan^(-1){x/(sqrt...

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  4. Evaluate each of the following: cot^(-1)1/(sqrt(3))-cos e c^(-1)(-2)+...

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  5. For the principal values, evaluate the following: cot^(-1)(-1)+cos e ...

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  6. Prove that: (i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqr...

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  7. Evaluate each of the following: sin^(-1)(s inpi/3) (ii) cos^(-1)(cos(...

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  8. If cos e c^(-1)x+cos e c^(-1)y+cos e c^(-1)z=-(3pi)/2, find the value ...

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  9. For the principal values, evaluate each of the following: tan^(-1)sqr...

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  10. Find the principal values of cot^(-1)sqrt(3) and cot^(-1)(-1)

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  11. For the principal values, evaluate the following: sin^(-1)(-(sqrt(3))...

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  12. The value of tan{cos^(-1)1/(5sqrt(2))-sin^(-1)4/(sqrt(17))} is (sqrt(2...

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  13. sin(cot^(-1)(tan(cos^(-1)x))) is equal to a) x b) sqrt(1-x^2) c) 1/x d...

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  14. Write the value of tan^(-1){2sin(2cos^(-1)(sqrt(3))/2)}dot

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  15. Write the principal value of cos^(-1)(cos680^0)dot

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  16. What is the principal value of sin^(-1)(-(sqrt(2))/2)?

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  17. Write the principal value of cos^(-1)(cos(2pi)/3)+sin^(-1)(s in(2pi)/3...

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  18. If tan^(-1)(sqrt(3))+cot^(-1)x=pi/2,t h e nfin dxdot

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  19. If sin^(-1)(1/3)+cos^(-1)x=pi/2,then find x

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  20. Write the value of 2sin^(-1)\ 1/2+cos^(-1)((a-b)/(a+b))

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