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If "sin"^(-1)(2a)/(1+a^(2))-"cos"^(-1)(1...

If `"sin"^(-1)(2a)/(1+a^(2))-"cos"^(-1)(1-b^(2))/(1+b^(2))="tan"^(-1)(2x)/(1-x^(2))`, then prove that `x=(a-b)/(1+ab)`.

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SHARAM PUBLICATION-INVERSE TRIGNOMETRIC FUNCTIONS-EXAMPLE
  1. Write the value of sin cos^(-1)tan sin^(-1)(1/sqrt2) in simplest form.

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  2. Find the value of sin[cot^(-1){tan(cos^(-1)x)}]

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  3. If "sin"^(-1)(2a)/(1+a^(2))-"cos"^(-1)(1-b^(2))/(1+b^(2))="tan"^(-1)(2...

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  4. What is the value of 2tan^(-1)(1/3)+tan^(-1)(1/7)?

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  5. Express the value of "tan"^(-1)(x/y)-"tan"^(-1)((x-y))/((x+y) in simpl...

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  6. What is the principal value of "cos"("cos"(2pi)/(3))+"sin"^(-1)("sin...

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  7. What is the principal value of "tan"^(-1)(0)and"tan"^(-1)(-1)

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  8. Find the principal value of :cos^(-1)(sqrt3/2).

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  9. Using the principal value, evaluate tan^ -1(1)+sin^(-1)(-1/2).

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  10. write the principal value of sin^(-1)[sin((3pi)/5)].

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  11. If "tan"^(-1)(sqrt(3))+"cot"^(-1)x=pi/(2), then find x.

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  12. Using the principal values, find the value of cos^(-1)cos((13pi)/(6)).

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  13. Show that "sin"^(-1)(4)/(5) +2"tan"^(-1)(1)/(3) =(pi)/(2).

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  14. Prove the following statements "cot"^(-1)9+"cosec"^(-1)sqrt(41)/(4)=...

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  15. Find the value of tan(cos^(-1)(4/5)+tan^(-1)(2/3)).

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  16. Show that sin^(-1)(1/sqrt(10))+cos^(-1)(2/sqrt5)=pi/4.

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  17. Prove statement"tan"^2 "cos"^(-1)1/sqrt3 +"cot"^2 "sin"^-1 1/sqrt5 =6

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  18. Solve: sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x.

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  19. Prove that: sec^2(tan^(-1)3)-cosec^2(cot^(-1)3)=0

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  20. Evaluate "cos"(2"cos"^(-1)x+"sin"^(-1)x) at x=1/(5), where 0le"cos"^(-...

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