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Solve: "cos"{2sin^(-1)(-x)}=0...

Solve: `"cos"{2sin^(-1)(-x)}=0`

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To solve the equation \( \cos(2 \sin^{-1}(-x)) = 0 \), we will follow these steps: ### Step 1: Set up the equation Let \( \theta = \sin^{-1}(-x) \). Therefore, we can rewrite the equation as: \[ \cos(2\theta) = 0 \] ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. If x=cos e c[tan^-1{"cos"(cot^-1(sec(sin^-1a)))}] and y="sec"[cot^-1{"...

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  2. Evaluate: sin{tan^(-1)(7/(24))}

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  3. Solve: "cos"{2sin^(-1)(-x)}=0

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  4. Solve : "cos"(sin^(-1)x)=1/6

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  5. Prove the following results: tan(cos^(-1)(4/5)+tan^(-1)(2/3))=(17)/6

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  6. If a , b , c >0 and s=(a+b+c)/2,p rov et h a t tan^(-1)sqrt((2a s)/(b...

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  7. If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+...

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  8. If cj &gt;0 for i=1,2,....., n prove that tan^(-1)((c1x-y)/(c1y+x)...

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  9. Evaluate: tan^(-1)((3sin2alpha)/(5+3cos2alpha))+tan^(-1)(1/4 tan alpha...

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  10. Prove that: sum(m=1)^ntan^(-1)((2m)/(m^4+m^2+2))=tan^(-1)((n^2+n)/(n^2...

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  11. Sum the following series to infinity: tan^(-1)1/(1+1+1^2)+tan^(-1)1/(...

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  12. Solve the equation: tan^(-1)sqrt(x^2+x)+sin^(-1)sqrt(x^2+x+1)=pi/2

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  13. If a1,a2,a3, an are in arithmetic progression with common difference d...

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  14. Prove that: tan^(-1)((1-x)/(1+x))-tan^(-1)((1-y)/(1+y))=sin^(-1)((y-x...

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  15. If x > y > z >0, then find the value of cot^(-1)(x y+1)/(x-y)+cot^(-1)...

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  16. Find the maximum and minimum values of (sin^(-1)x)^3+(cos^(-1)x)^3, wh...

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  17. the greatest and least values of (sin^(-1) x)^2+(cos^(-1)x)^2

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  18. Solve : 4sin^(-1)x=pi-cos^(-1)x

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  19. If (sin^(-1)x)^2+(cos^(-1)x)^2=(17pi^2)/(36) , find xdot

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  20. Prove that : tan^(-1)2+tan^(-1)3=(3pi)/4

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