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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))) + 1/2 cos^(-1) ((1-y^(2))/(1+ y^(2)))}`

Text Solution

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The correct Answer is:
`(1+xy)/(x-y)`
NA
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RESONANCE ENGLISH-RELATION, FUNCTION & ITF-SUBJECTIVE_TYPE
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  2. tan^(-1)x + cot^(-1) (1/x) + 2tan^(-1)z =pi, then prove that x + y + 2...

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  3. If cos^(-1)x+2sin^(-1)x+3cot^(-1)y+4tan^(-1)y=4sec^(-1)z+5cosec^(-1)z,...

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  4. Prove each of the following tan^(-1) x=-pi +cot^(-1) 1/x=sin^(-1) (x...

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  5. Express sin^(-1)x in terms of (i) cos^(-1)sqrt(1-x^(2)) (ii) "tan"^(-1...

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  6. Express in terms of : "tan"^(-1)(2x)/(1-x^(2) to tan^(-1)x for xgt1

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  7. sin^(-1)(2xsqrt(1-x^2)),x in [1/sqrt2,1] is equal to

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  8. Express in terms of : cos^(-1)(2x^(2)-1) to cos^(-1)x for -1lexlt0

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

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  10. Solve for x : cos(2sin^(-1)x)=1/3

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  11. Solve for x : cot^(-1)x+tan^(-1)3=(pi)/2

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  12. Solve : tan^(-1)(x-1)/(x-2)+tan^(-1)(x+1)/(x+2)=pi/4

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  13. Solve sin^(-1)x+sin^(-1)2x=pi/3dot

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  14. Prove that : sin^(-1)8/(17)+sin^(-1)3/5=sin^(-1)(77)/(85)=tan^(-1)((77...

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  15. Prove that : "tan"^(-1)3/4+"sin"^(-1)5/13="cos"^(-1)33/65

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  16. Prove: sin^(-1)(1/sqrt5)+cot^(-1)3=pi/4

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  17. Prove that : tan^(-1)(1/5)+tan^(-1)(1/7)+tan^(-1)(1/3)+tan^(-1)(1/8)=p...

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  18. Find the sum of each of the following series :(i) tan^-1(1/(x^2+x+1))+...

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  19. Find the sum of the series :tan^- 1(1/3)+tan^- 1(2/9)+....+tan^- 1((2^...

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  20. Find the sum of infinite series s = sin^(-1) ( 1/sqrt2) + sin ^(-1) ...

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