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Prove that: sin^(-1)((63)/(65))=sin^(-1)...

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

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R.H.S=`tan^(-1)((5/13)/sqrt(1-(5/13)^2)+tan^(-1)sqrt(1-(3/5)^2)/(3/5)`
=`tan^(-1)(5/12)+tan^(-1)(4/3)`
=`tan^(-1)((5/12+4/3)/(1-5/12.4/3))`
=`tan^(-1)(63/16)`
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. cos(sin^-1 (3/5)+ cot^-1(3/2)) = 6/(5sqrt13)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. Find the principal value of each of the following: (i) sin^(-1)(-(s...

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  19. Find the principal value of each of the following: (i) sin^(-1)((sq...

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  20. If tan^(-1)x = y then

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