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If cos^(-1)x+cos^(-1)y+cos^(-1)=pi, prov...

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

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To prove that if \( \cos^{-1} x + \cos^{-1} y + \cos^{-1} z = \pi \), then \( x^2 + y^2 + z^2 + 2xyz = 1 \), we can follow these steps: ### Step 1: Rewrite the Given Equation We start with the equation: \[ \cos^{-1} x + \cos^{-1} y + \cos^{-1} z = \pi \] ...
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If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi , then

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

If (i) cos^(-1) x + cos^(-1) y + cos^(-1) z = pi , prove that : x^(2) +y^(2) +z^(2) + 2xyz = 1 (ii) If sin^(-1) x + sin^(-1) y + sin^(-1) z = pi/2 , prove that : x^(2) +y^(2) +z^(2) +2xyz = 1

If cos^(-1)x +cos^(-1)y +cos^(-1)z =3pi then x+y+z is :

If cos^(-1)x + cos^(-1)y + cos^(-1)z = pi , then x^(2) + y^(2) + z^(2) + 2xyz is :

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi, then x^(2)+y^(2)+z^(2)+2xyz=12(sin^(-1)x+sin^(-1)y+sin^(-1)z)=cos^(-1)x+cos^(-1)y+cos^(-1)zxy+yz+zx=x+y+z-1(x+(1)/(x))+(y+(1)/(y))+(z+(1)/(z))>=6

If cos^(-1)x+cos^(-1)y+cos^(-1)z=pi, then x^(2)+y^(2)+z^(2)+xyz=0x^(2)+y^(2)+z^(2)+2xyz=0x^(2)+y^(2)+z^(2)+xyz=1x^(2)+y^(2)+z^(2)+2xyz=1

If cos^(-1)x + cos^(-1)y - cos^(-1) z = 0 , then show that x^(2) + y^(2) + z^(2) - 2xyz = 1

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

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

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  4. If cos^(-1)(x/a)+cos^(-1)(y/b)=alpha, prove that (x^2)/(a^2)-2(x y)/(...

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  5. Solve sin^(-1)x+sin^(-1)2x=pi/3dot

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  6. Solve the following equations: sin^(-1)(3x)/5+sin^(-1)(4x)/5=sin^(-1)...

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  7. Prove that sin^(-1)(8/(17))+sin^(-1)(3/5)=cos^(-1)((36)/(85))

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  8. The value of tan^-1(1/3)+tan^-1(2/9)+tan^-1(4/33)+tan^-1(8/129)+....n ...

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  9. Find the value of tan^(-1)(x/y)-tan^(-1)((x-y)/(x+y))

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  10. Prove that: tan^(-1)(1/2tan2A)+tan^(-1)(cota)+tan^(-1)(cot^3A)={0,ifp...

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  11. "If"sin{cot^(-1)(x+1)}=cos(tan^(-1)x), then find x.

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  12. Solve the following equation for x : "cos"(tan^(-1)x)=sin(cot^(-1)3/...

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  13. Write each of the following in the simplest form: cot^(-1){a/(sqrt(x...

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  14. Evaluate: sin(cot^(-1)x) (ii) cos(tan^(-1)x)

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  15. Simplify each of the following: sin^(-1)((sinx+cosx)/(sqrt(2)))

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  16. Evaluate the following: sin^(-1)(sin 10)

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  17. Prove that: sec^2(tan^(-1)2)+cos e c^2(cot^(-1)3)=15 and tan^2(s...

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  18. Prove that: "sin"[cot^(-1){"cos"(tan^(-1)x)}]=sqrt((x^2+1)/(x^2+2)) ...

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  19. Evaluate: sin(cos^(-1)3/5+cos e c^(-1)(13)/5)

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  20. Find the value of the expression sin[cot^(-1){cos(tan^-1 1)}]

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