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

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

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`= sin [tan^(-1) (cot 2 theta) + cos^(-1) cos 2 theta]`
`= sin [tan^(-1) tan ((pi/2) – 2 theta) + 2 theta]`
` = sin ((pi / 2) – 2 theta + 2 theta)`
` = sin (pi/2)` ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Prove that: 2tan^(-1)(1/2)+tan^(-1)(1/7)=tan^(-1)((31)/(17))

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  2. Prove that: tan^(-1)((1-x^2)/(2x))+cot^(-1)((1-x^2)/(2x))pi/2

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

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  4. If sin^(-1) ((2a)/(1+a^2))+ sin^(-1) ((2b)/(1+b^2)) = 2 tan^(-1)x then...

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  5. Show that :2tan^(-1)x+sin^(-1)((2x)/(1+x^2)) is constant for xgeq1, fi...

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  6. Find the value of: tan^(-1)[2cos(2sin^(-1)(1/2))]

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  7. Find the value of cos(sec^(-1)x+"c o s e c"^(-1)x) , |x|geq1

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  8. Find the value of tan^(-1)((x-2)/(x-1))+tan^(-1)((x+2)/(x+1))=pi/4

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  9. Solve the following equation for x:tan^(-1)(1/4)+2tan^(-1)(1/5)+tan^(-...

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

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

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

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  13. Solve for x : cos^(-1)((x^2-1)/(x^2+1))+1/2tan^(-1)((2x)/(1-x^2))=(2pi...

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  14. prove that 2tan^-1(sqrt((a-b)/(a+b))tan(theta/2))=cos^-1((acostheta+b)...

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  15. Show that (tan^-1)(2ab)/(a^2-b^2)+(tan^-1)(2xy)/(x^2-y^2)=(tan^-1) (2a...

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  16. For any a ,\ b ,\ x ,\ y >0 , prove that : 2/3tan^(-1)((3a b^2-a^3)/(b...

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  17. Write the value of sin^(-1)(-(sqrt(3))/2)+cos^(-1)(-1/2) .

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  18. Write the difference between maximum and minimum values of sin^(-1)...

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  19. If sin^(-1)x+sin^(-1)y+sin^(-1)z=(3pi)/2 , then write the value of ...

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  20. If x >1 , then write the value of sin^(-1)((2x)/(1+x^2)) in terms o...

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