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If cos^(-1)x+2sin^(-1)x+3cot^(-1)y+4tan^...

If `cos^(-1)x+2sin^(-1)x+3cot^(-1)y+4tan^(-1)y=4sec^(-1)z+5cosec^(-1)z`, then prove that `sqrt(z^2-1)=(sqrt(1+x^2)-xy)/(x+ysqrt(1-x^2))`

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RESONANCE-RELATION, FUNCTION & ITF-SUBJECTIVE_TYPE
  1. Find the value of sin^(-1)(cos(sin^(-1)x))+cos^(-1)(sin(cos^(-1)x))

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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. Consider f(x)=tan^(-1)(2/x),g(x)=sin^(-1)(2/(sqrt(4+x^(2)))) and h(x)=...

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

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  6. Prove each of the following relation: cos^(-1)x=sec^(-1)1/x=pi-sin^(...

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

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  8. Express in terms of : sin^(-1)(2xsqrt(1-x^(2))) to sin^(-1)x for 1gexg...

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

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  10. Simplity tan{1/2sin^(-1)((2x)/(1+x^(2)))+1/2cos^(-1)(1-y^(2))/(1+y^(2)...

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

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

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

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

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

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

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

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  18. Prove that ta n^-1 1/3 + ta n ^-1 1/5 + ta n ^-1 1/7 + ta n ^-1 1/8 =...

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

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

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