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Solve the following equations: sin[2...

Solve the following equations: `sin[2cos^(-1)"{"cot"("2tan^(-1)x"}]"=0`

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To solve the equation \[ \sin\left[2\cos^{-1}\left(\cot\left(2\tan^{-1}x\right)\right)\right] = 0, \] we will follow these steps: ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. In a A B C , , if C is a right angle, then tan^(-1)(a/(b+c))+tan^(-1...

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  2. If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(...

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  3. Solve the following equations: sin[2cos^(-1)"{"cot"("2tan^(-1)x"}]...

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  4. Solve the equation of x:sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x

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  5. cos(sin^-1 (3/5)+ cot^-1(3/2)) = 6/(5sqrt13)

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  6. Prove that : tan^(-1)((63)/(16))=sin^(-1)((5)/(13))+cos^(-1)((3)/(5))

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  7. Prove that: sin^(-1)((63)/(65))=sin^(-1)(5/(13))+cos^(-1)(3/5)

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  8. Solve the following equation for x : 3sin^(-1)(2x)/(1+x^2)-4cos^(-1)(...

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  9. Solve the following equation for x: tan^(-1)((2x)/(1-x^2))+cot^(-1)...

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  10. Solve for x : 2tan^(-1)(sinx)=tan^(-1)(2secx),\ x!=pi/2

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  11. Prove that: sin{tan^(-1)((1-x^2)/(2x))+cos^(-1)((1-x^2)/(1+x^2))}=1

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  12. Find the principal values of (a) sin^(-1)((sqrt(3))/2) (b) sin^(-1)(...

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  13. Find the principal values of sin^(-1)(1/2)

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  14. Find the value of sin^(-1)[cos{sin^(-1)(-(sqrt(3))/2)}] .

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  15. Find the domain of the function f(x)=sin^(-1)(2x-3) .

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  16. Find the domain of f(x)=sin^(-1)(-x^2)dot

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  17. Find the domain of f(x)=sin^(-1)x+cosx

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  18. Find the domain of the function f(x)=sin^(-1)sqrt(x-1)

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  19. If x , y , z in [-1,1] such that sin^(-1)x+sin^(-1)y+sin^(-1)z=-(3pi)/...

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  20. Let x ,\ y ,\ z in [-1,\ 1] such that sin^(-1)x+sin^(-1)y+sin^(-1)z=(3...

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