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Show that "tan"^(-1)sqrt(x)=1/(2)"cos"...

Show that
`"tan"^(-1)sqrt(x)=1/(2)"cos"^(-1)((1-x)/(1+x)),x in[0,1]`.

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Prove that tan^(-1)sqrt(x) =(1)/(2) cos^(-1)((1-x)/(1+x)), x in (0, 1) .

Show that "sin"^(-1)(2xsqrt(1-x^(2)))=2"cos"^(-1)x,1/(sqrt(2))lexle1 .

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

Solve: 3 "sin"^(-1) (2x)/(1+x^2) -4"cos"^(-1) (1-x^2)/(1+x^2) +2 "tan"^(-1) (2x)/(1-x^2) = pi/3

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

Prove the following "tan"^(-1)((1-x)/(1+x))-"tan"^(-1)((1-y)/(1+y))="sin"^(-1)((y-x)/(sqrt(1+x^(2))sqrt(1+y^(2)))) .

Differentiate tan^(-1)((sqrt(1+x^2)-1)/x) w.r.t sin^(-1)((2x)/(1+x^2)) when x!=0 .

Prove that cos tan^(-1)sin cot^(-1)x=sqrt((1+x^2)/(2+x^2) .

Prove that 1/2cos^-1x=sin^-1sqrt((1-x)/2)=cos^-1sqrt((1+x)/2) .

Solve equation "tan"^(-1) (x-1)/(x+1) ="tan"^(-1) (2x-x)/(2x+1) = "tan"^(-1) 23/36

ARIHANT PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS -Part II (Sample Question )
  1. Evaluate "cot"("tan"^(-1)a+"cot"^(-1)a).

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  2. Evaluate "cos"(2"cos"^(-1)x+"sin"^(-1)x) at x=1/(5), where 0le"cos"^(-...

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

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  4. Evaluate "tan"("sin"^(-1)3/(5)+"cot"^(-1)3/(2)).

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  5. Write the value of "tan"(2"tan"^(-1)1/(5)).

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  6. Solve "sin"^(-1)(3/(5))+"sin"^(-1)(8/(17)).

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  7. Find the value of "cos"^(-1)((-7)/(25))+"cos"^(-1)(3/(5)).

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  8. Evaluate "sin"(3"sin"^(-1)0.4)

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  9. Find the value of "tan"1/(2)["sin"^(-1)(2x)/(1+x^(2))+"cos"^(-1)(1-y...

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  10. Show that "tan"^(-1)sqrt(x)=1/(2)"cos"^(-1)((1-x)/(1+x)),x in[0,1].

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  11. Write the simplest form of "sec"^(-1)(sqrt(1+x^(2))).

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  12. Express the expression in simplest form "cos"^(-1)((sqrt(4-x^(2)))/(2)...

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  13. Express the expression in simplest form "tan"^(-1)[x/(sqrt(a^(2)-x^(2)...

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  14. Write the simplest form "tan"^(-1)[(3a^(2)x-x^(3))/(a^(3)-3ax^(2))],ag...

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  15. Show that "sin"^(-1)(2xsqrt(1-x^(2)))=2"cos"^(-1)x,1/(sqrt(2))lexle1.

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  16. Prove that cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

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  17. Prove that cos^(-1)(x)+ cos^(-1){(x)/(2)+sqrt(3-3x^(2))/(2)}=(pi)/(3).

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  18. If "sin"("sin"^(-1)1/(5)+"cos"^(-1)x)=1, then find the value of x.

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

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  20. Solve for x, "tan"^(-1)3x+"tan"^(-1)2x=pi/(4).

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