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Find the value of "tan"1/(2)["sin"^(-1...

Find the value of
`"tan"1/(2)["sin"^(-1)(2x)/(1+x^(2))+"cos"^(-1)(1-y^(2))/(1+y^(2))],|x|lt1,ygt0andxylt1`.

Text Solution

Verified by Experts

The correct Answer is:
`(x+y)/(1-xy)`
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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -Part II (Sample Question )
  1. Evaluate "cot"("tan"^(-1)a+"cot"^(-1)a).

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

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  3. Prove that "tan"^(-1)2/(11)+"tan"^(-1)7/(24)="tan"^(-1)1/(2).

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  4. Evaluate "tan"("sin"^(-1)3/(5)+"cot"^(-1)3/(2)).

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  5. Write the value of "tan"(2"tan"^(-1)1/(5)).

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  6. Solve "sin"^(-1)(3/(5))+"sin"^(-1)(8/(17)).

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  7. Find the value of "cos"^(-1)((-7)/(25))+"cos"^(-1)(3/(5)).

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  8. Evaluate "sin"(3"sin"^(-1)0.4)

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  9. Find the value of "tan"1/(2)["sin"^(-1)(2x)/(1+x^(2))+"cos"^(-1)(1-y...

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  10. Show that "tan"^(-1)sqrt(x)=1/(2)"cos"^(-1)((1-x)/(1+x)),x in[0,1].

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  11. Write the simplest form of "sec"^(-1)(sqrt(1+x^(2))).

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  12. Express the expression in simplest form "cos"^(-1)((sqrt(4-x^(2)))/(2)...

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  13. Express the expression in simplest form "tan"^(-1)[x/(sqrt(a^(2)-x^(2)...

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  14. Write the simplest form "tan"^(-1)[(3a^(2)x-x^(3))/(a^(3)-3ax^(2))],ag...

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  15. Show that "sin"^(-1)(2xsqrt(1-x^(2)))=2"cos"^(-1)x,1/(sqrt(2))lexle1.

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  16. Prove that cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

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  17. Prove that cos^(-1)(x)+ cos^(-1){(x)/(2)+sqrt(3-3x^(2))/(2)}=(pi)/(3).

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  18. If "sin"("sin"^(-1)1/(5)+"cos"^(-1)x)=1, then find the value of x.

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  19. Solve the following equation: "cos"("tan"^(-1)x)="sin"("cot"^(-1)3/(...

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  20. Solve for x, "tan"^(-1)3x+"tan"^(-1)2x=pi/(4).

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