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Prove that "tan"^(-1)(1/4)+"tan"^(-1)(2/...

Prove that `"tan"^(-1)(1/4)+"tan"^(-1)(2/9)=1/2"tan"^(-1)(4/3)`.

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Prove that "tan"^(-1)2/(11)+"tan"^(-1)7/(24)="tan"^(-1)1/(2) .

Prove that "tan"^(-1)1/(2)+"tan"^(-1)1/(5)+"tan"^(-1)1/8=pi/(4) .

Prove that: tan^(-1)(3/4)+tan^(-1)(3/5)-tan^(-1)(8/19)=pi/4

Prove statement "tan"^(-1) 1/7+ "tan"^(-1)1/13="tan"^(-1) 2/9

Prove that tan^(-1)((1)/(5)) +tan^(-1)((1)/(7)) +tan^(-1)((1)/(3)) +tan^(-1)((1)/(8)) = (pi)/(4) .

If r^2 =x^2 +y^2+z^2, "Prove that" "tan"^(-1) (yz)/(xr) ="tan"^(-1) (zx)/(yr) +"tan"^(-1) (xy)/(zr) =pi/2

Show that 2 tan^-1(1/4) + 2 tan^-1 (2/9) = tan^-1(4/3) .

Prove statement "tan"(-1)1/2 +"tan"^(-1) 1/5 +"tan"^(-1) 1/8 = pi/4

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

Prove that tan^(-1)(1)+tan^(-1)(2) +tan^(-1)(3) =pi .

ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -Part II (QUESTIONS FOR PRACTICE)
  1. Write "tan"^(-1)(("cos"x-"sin"x)/("cos"x+"sin"x)),xltpi in the simples...

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  2. Write "cot"^(-1)(1/(sqrt(x^(2)-1))),|x|gt1 in simplest form.

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  3. Prove that "tan"^(-1)(1/4)+"tan"^(-1)(2/9)=1/2"tan"^(-1)(4/3).

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  4. Show that "sin"^(-1)(8/17)+"sin"^(-1)(3/5)="cos"^(-1)(36/85).

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  5. If "tan"^(-1)x+"tan"^(-1)y=pi/4,xylt1, then write the value of x+y+x...

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  6. Prove that "tan"^(-1)1/(2)+"tan"^(-1)1/(5)+"tan"^(-1)1/8=pi/(4).

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  7. Show that tan((1)/(2)"sin"^(-1)(3)/(4))=(4-sqrt(7))/(3).

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

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  9. If "sin"^(-1)(1-x)(1)-2"sin"^(-1)x=pi/(2), then find the value of x.

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  10. If "tan"^(-1)((x-2)/(x-4))+"tan"^(-1)((x+2)/(x+4))=pi/(4), then find t...

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  11. Solve for x, "tan"^(-1)((2x)/(1-x^(2)))+""cot"^(-1)((1-x^(2))/(2x))=...

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  12. Find the value of expression "sin"(2"tan"^(-1)1/(3))+"cos"("tan"^(-1...

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  13. Solve for x, 2 tan ^(-1)(cos x) =tan^(-1) (2"cosec"x).

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  14. If "tan"^(-1)a+"tan"^(-1)b+"tan"^(-1)c=pi, then prove that a+b+c=abc.

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  15. Solve for x, "tan"^(-1)x+2"cot"^(-1)x=(2pi)/(6).

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  16. Prove that (9pi)/(8) -(9)/(4) sin^(-1)((1)/(3)) =(9)/(4) sin^(-1)((2sq...

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  17. Prove that following cot^(-1)((xy+1)/(x-y)) +cot^(-1)((yz+1)/(y-z))+...

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  18. If "cos"^(-1)alpha+"cos"^(-1)beta+"cos"^(-1)gamma=3pi, then find alpha...

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  19. Prove that "tan"^(-1)((sqrt(1+x^(2))+sqrt(1-x^(2)))/(sqrt(1+x^(2))-s...

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  20. Prove that 2"tan"^(-1)(1/(5))+"sec"^(-1)((5sqrt(2))/(7))+2"tan"^(-1)(1...

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