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Directions (Q. Nos. 16-25) Prove the fol...

Directions (Q. Nos. 16-25) Prove the following
`"cos"^(-1)x="tan"^(-1)[(sqrt(1-x^(2)))/(x)]`.

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ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -CHAPTER PRACTICE
  1. Solve for x, "sin"^(-1)((2alpha)/(1+alpha^(2)))+"sin"^(-1)((2beta)/(...

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  2. Show that "sin"^(-1)(2xsqrt(1-x^(2)))=2"sin"^(-1)x.

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  3. Directions (Q. Nos. 16-25) Prove the following "cos"^(-1)x="tan"^(-1...

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  4. Directions (Q. Nos. 16-25) Prove the following 2"tan"^(1)1/(2)+"tan"...

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  5. Prove that tan^(-1)((1)/(5)) +tan^(-1)((1)/(7)) +tan^(-1)((1)/(3)) +...

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  6. Directions (Q. Nos. 16-25) Prove the following "sin"^(-1)(5/(13))+"c...

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  7. Directions (Q. Nos. 16-25) Prove the following "cos"["tan"^(-1){"sin...

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  8. Directions (Q. Nos. 16-25) Prove the following "cos"["sin"^(-1)(3/(5...

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  9. Directions Prove the following "tan"^(-1)1/(4)+"tan"^(-1)2/(9)=1/(2)...

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  10. Directions Prove the following "tan"^(-1)((sqrt(1+"cos"x)+sqrt(1-"c...

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  11. Prove the following "tan"^(-1)((1-x)/(1+x))-"tan"^(-1)((1-y)/(1+y))=...

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  12. Directions (Q. Nos. 16-25) Prove the following "cos"(2"tan"^(-1)1/(7...

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  13. Simplify the following: "tan"^(-1)[x/(sqrt(a^(2)-x^(2)))],|x|lta.

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

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  15. Directions (Q. Nos. 27 and 28) Solve the following equations: "tan"...

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  16. Prove that tan^(-1)((cosx)/(1+sin x)) =(pi)/(4)-(x)/(2), x in (-(pi...

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  17. Prove that tan{(pi)/(4)+(1)/(2) "cos"^(-1)(a)/(b)}+tan{(pi)/(4)-(1)/(2...

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  18. Find the value of 4"tan"^(-1)1/(5)-"tan"^(-1)1/(239).

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  19. Find the value of "tan"^(-1)("tan"(5pi)/(6))+"cos"^(-1)("cos"(13pi)/(6...

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  20. Prove that 2"tan"^(-1)(sqrt((a-b)/(a+b))"tan"theta/(2))="cos"^(-1)((...

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