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Write each of the following in the simplest form: `cot^(-1){a/(sqrt(x^2-a^2))},\ \ |x|> a` (ii) `tan^(-1){x+sqrt(1+x^2)},\ \ x in R`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Evaluate each of the following: cot^(-1)(cotpi/3) (ii) cot^(-1)(cot...

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  2. Evaluate each of the following: cot^(-1)(cot((19pi)/6)) (ii) cot^(-1...

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  3. Write each of the following in the simplest form: cot^(-1){a/(sqrt(...

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  4. Write each of the following in the simplest form: tan^(-1){sqrt(1+x...

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  5. Write each of the following in the simplest form: tan^(-1){(sqrt(1+x...

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  6. Write each of the following in the simplest form: tan^(-1){x/(a+sqrt...

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  7. Evaluate int(sin5x+ e^(5x))\dx

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  8. Evaluate int\tan5x\dx

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  9. Evaluateint(x-2)(x-1)\dx

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  10. Evaluateint(x-1)(x-3)\dx

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  11. Evaluate int(2-x)(1-x)\dx

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  12. Evaluate each of the following: tan(tan^(-1)3/4) (ii) tan(sin^(-1)5...

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  13. Evaluate each of the following: tan("c o s e c"^(-1)(13)/5) (ii) tan...

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  14. Evaluate: sin(cot^(-1)x) (ii) cos(tan^(-1)x)

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  15. Evaluate : cos(sin^(-1)(1/4)+sec^(-1)(4/3))

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  16. Evaluate: sin(cos^(-1)3/5+cos e c^(-1)(13)/5)

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  17. Find the value of the expression sin[cot^(-1){cos(tan^11)}]

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  18. Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(s...

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  19. Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(s...

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  20. Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2)) c...

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