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sin^(-1)(1-x)-2sin^(-1)x=pi/2 , then x i...

`sin^(-1)(1-x)-2sin^(-1)x=pi/2` , then x is equal to (A) `0,1/2` (B) `1,1/2` (C) 0 (D) `1/2`

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To solve the equation \( \sin^{-1}(1-x) - 2\sin^{-1}(x) = \frac{\pi}{2} \), we will follow these steps: ### Step 1: Substitute \( \sin^{-1}(x) \) with \( \theta \) Let \( \sin^{-1}(x) = \theta \). Then, we have: \[ x = \sin(\theta) \] ...
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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Prove the following: 4tan^(-1)1/5-tan^(-1)1/(70)+tan^(-1)1/(99)=pi/4 ...

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  2. Evaluate: tan{1/2cos^(-1)(sqrt5/3)}

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  3. sin^(-1)(1-x)-2sin^(-1)x=pi/2 , then x is equal to (A) 0,1/2 (B) 1,1...

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  4. If y=cot^(-1)(sqrt(cos"x"))-tan^(-1)(sqrt(cos"x")), prove that siny=ta...

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  5. Evaluate: tan(2tan^(-1)(1/5))

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  6. Prove that sin^-1[3/5]+sin^-1[4/5]=pi/2

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

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  8. Find the value of expression: sin(2tan^(-1)(1/3))+cos(tan^(-1)2sqrt(2)...

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  9. Find the principal value of the following: """"" sin^(-1){cos(sin^(...

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

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

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  12. Find the domain of f(x)=sin^(-1)x+cosxdot

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

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

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

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

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  17. Find the domain of function: f(x)=sin^(-1)sqrt(x^2-1)

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  18. Prove that: 2tan^(-1) {1/2}+tan^(-1) {1/7}=tan^(-1) {(31)/(17)}

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  19. Solve the equation: cos^(-1)(a/x)-cos^(-1)(b/x)=cos^(-1)(1/b)-cos^(-1)...

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  20. If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi, prove that x^2+y^2+z^2+2x y z=1.

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