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Prove the following statements "cos"" ...

Prove the following statements
`"cos"" (tan"^(-1)"(cot"" (sin"^(-1)x)))=x`

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Prove statement "cos"" tan"^(-1) " cot sin"^(-1) x =x

Express the value of the following in simplest form. "sin("" cot"^(-1)"( cos""( tan"^(-1)x)))

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

Solve the following equation: "cos"("tan"^(-1)x)="sin"("cot"^(-1)3/(4)) .

Directions (Q. Nos. 16-25) Prove the following "cos"(2"tan"^(-1)1/(7))="sin"(4"tan"^(-1)1/(3)) .

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

Directions (Q. Nos. 16-25) Prove the following "cos"["sin"^(-1)(3/(5))+"cot"^(-1)(3/(2))]=6/(5sqrt(13)) .

Directions Prove the following "tan"^(-1)1/(4)+"tan"^(-1)2/(9)=1/(2)"cos"^(-1)3/(5)=1/(2)"sin"^(-1)4/(5) .

Write whether the following statements are true or false. The equation "tan"^(-1)("cot"x)=2x has exactly two real solutions.

Express the value of the following in simplest form. "sin"(2"tan"^(-1)sqrt((1-x)/(1+x)))

ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -ODISHA BUREAU.S TEXTBOOK SOLUTIONS
  1. Prove statement "cos"^(-1) 12/13 +2"cos"^(-1) sqrt(64/65) +"cos"^(-1) ...

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  2. Prove statement"tan"^2 "cos"^(-1)1/sqrt3 +"cot"^2 "sin"^-1 1/sqrt5 =6

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  3. Prove the following statements "cos"" (tan"^(-1)"(cot"" (sin"^(-1)x)...

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  4. Prove statement "cot"^(-1)("tan"2x) +"cot"^(-1)(-"tan"2x) = pi

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  5. Prove statement "tan"^(-1) x +"cot"^(-1)(x+1)="tan"^(-1)(x^2+x+1)

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  6. Prove statement "tan"^(-1)((a-b)/(1+ab)) +"tan"^(-1)((b-c)/(1+bc)) ="...

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  7. Prove statement "cot"^(-1)(pq+1)/(p-q) +"cot"^-1(qr+1)/(q-r) +"cot"^(-...

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  8. Prove statement"tan"^(-1) (a-b)/(1+ab)+"tan"^(-1)(b-c)/(1+bc) +"tan"^-...

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  9. Prove the following "tan"^(-1)(2a-b)/(bsqrt(3))+"tan"^(-1)(2b-a)/(as...

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  10. Prove the "tan"^(-1) 1/(x+y) + "tan"^(-1) y/(x^2=xy+1) ="tan"^(-1)1/x

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  11. Prove the "sin"^(-1) sqrt((x-q)/(p-q))="cos"^(-1)sqrt((p-x)/(p-q))="co...

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  12. Prove the sin^2(sin^(-1) x+sin^(-1) y+sin^(-1)z) =cos^2 (cos^(-1)x +c...

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  13. Prove the "tan"("tan"^(-1)x +"tan"^(-1) y + "tan"^(-1)z)="cot"("cot"^-...

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  14. If "sin"^(-1)x+"sin"^(-1)y+"sin"^(-1)z=pi, show that xsqrt(1-x^(2))+ys...

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  15. If "tan"^(-1) x +"tan" ^(-1) y +"tan"^(-1)z -pi show that x+y+z=xyz.

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  16. If "tan"^(-1)x+"tan"^(-1)y+"tan"^(-1)z=pi/(2), show that xy+yz+zx=1

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  17. If r^2 =x^2 +y^2+z^2, "Prove that" "tan"^(-1) (yz)/(xr) ="tan"^(-1) (...

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  18. In a DeltaABC, if mangleA=90^(@), prove that "tan"^(-1)b/(a+c)+"tan"^(...

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  19. Solve for x, cos (2sin^(-1)x)=(1)/(9), x gt 0.

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  20. Solve sin^(-1)x +sin^(-1)(1-x) =(pi)/(2).

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