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Find the principal value of cos^(-1){sin...

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

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Verified by Experts

We know that,
`cos ^{-1} frac{1}{2}=frac{pi}{3}`
Thus,
`cos ^{-1} [sin (cos ^{-1} frac{1}{2})]`
`=cos ^{-1} (sin frac{pi}{3})`
...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Find the principal values of sec^(-1)2/(sqrt(3)) and sec^(-1)(-2)

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  2. Find the domain of sec^(-1)(2x+1)

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

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

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

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  6. For the principal values, evaluate each of the following: tan^(-1){2co...

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

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  8. Find the domain of sec^(-1)(3x-1) + sec^(-1)x-tan^(-1)x

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

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

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

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

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

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

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  16. Prove that 2sin^-1[3/5]-tan^-1[17/31]=pi/4

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

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

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  19. Find the principal value of each of the following: (i)sin^(-1)1/2-2s...

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

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