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If x , y ,z in [-1,1] such that cos^(-1)...

If `x , y ,z in [-1,1]` such that `cos^(-1)x+cos^1y+cos^(-1)z=3pi,` then find the values of (1). `x y+y z+z y` and (2).`x(y+z)+y(z+x)+z(x+y)`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Find the domain of sec^(-1)(2x+1)

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  2. Find the principal value of cos^(-1){sin"{"cos^(-1)1/2")"}

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  3. If x , y ,z in [-1,1] such that cos^(-1)x+cos^1y+cos^(-1)z=3pi, then f...

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  4. Evaluate tan ^ (-1) {sin (-pi/2)}

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  5. For the principal values, evaluate each of the following: (i) tan^(-1)...

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  6. For the principal values, evaluate each of the following: "tan^(-1)sq...

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  7. Find the domain of sec^(-1)(3x-1) (ii) sec^(-1)x-tan^(-1)x

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  8. Show that cos^(-1) ((cos alpha+cos beta)/(1+cosalpha cosbeta))=2 tan^(...

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  9. Show taht 2tan^-1(tan(alpha/2)tan(pi/4-beta/2))=tan^-1((sinalphacosbet...

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  10. Prove the following: 4tan^(-1)1/5-tan^(-1)1/(70)+tan^(-1)1/(99)=pi/4 ...

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

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

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

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

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

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

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

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

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

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