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Directions Prove the following "tan"^...

Directions Prove the following
`"tan"^(-1)((sqrt(1+"cos"x)+sqrt(1-"cos"x))/(sqrt(1+"cos"x)-sqrt(1-"cos"x)))=pi/(4)+x/(2)`, if `piltxlt(3pi)/(2)`.

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Prove that "tan"^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-sqrt(1-x^(2))))=pi/(4)+1/(2)"cos"^(-1)x^(2) .

Prove that cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=(x)/(2), 0 lt x lt (pi)/(2), or x in (0, (pi)/(4)) .

Simplify "tan"^(-1)[sqrt((1-"cos"x)/(1+"cos"x))],xltpi .

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. Evaluate tan^(-1)((3sin 2alpha)/(5+3cos2alpha)) +tan^(-1)((1)/(4)tan a...

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