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The principal value of sin^(-1)[cos(sin^...

The principal value of `sin^(-1)[cos(sin^(-1)'1/2)]` is `pi/3`.

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`sin^(-1)[cos(sin^(-1)'1/2)]`
`=sin^(-1)((sqrt 3)/2)`
`=sin^(-1) sin frac{pi}{3}`
`=frac{pi}{3}`
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Write the value of cos(sin^(-1)x+cos^(-1)x) , |x|lt=1 .

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  2. The value of tan((sin^(-1)x+cos^(-1)x)/(2)), when x = (sqrt(3))/(2), i...

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  3. The principal value of sin^(-1)[cos(sin^(-1)'1/2)] is pi/3.

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  4. Find the set of values of "c o s e c"^(-1)((sqrt(3))/2)

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  5. Write the value of tan^(-1)(1/x) for x<0 in terms of cot^(-1)(x) .

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  6. The value of cot^(-1)(-x) x in R in terms of cot^(-1)x is "…….."

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  7. Write the value of cos((tan^(-1)x+cot^(-1)x)/3) , when x=-1/(sqrt(3)) ...

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  8. If cos(tan^(-1)x+cot^(-1)sqrt(3))=0 , find the value of xdot

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  9. Find the value of 2\ sec^(-1)2+sin^(-1)(1/2) .

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  10. If cos((sin^(-1)2)/5+cos^(-1)x)=0 find the value of xdot

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  11. Find the value of the following: cos^(-1)(cos(13pi)/6)

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  12. 8. Find the principal value of tan^-1( tan (9pi)/8)

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  13. If tan^(-1){(sqrt(1+x^2)-sqrt(1-x^2))/(sqrt(1+x^2)+sqrt(1-x^2))}=alpha...

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  14. The value of tan{cos^(-1)1/(5sqrt(2))-sin^(-1)4/(sqrt(17))} is (sqrt(2...

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  15. The value of 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x) is equal to cot^...

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

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  17. Find the number of positive integral solution of the equation tan^(-1)...

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  18. If sin^(-1)x-cos^(-1)x=pi/6 , then x= 1/2 (b) (sqrt(3))/2 (c) -1/2 (d...

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  19. sin[cot^(-1){tan(cos^(-1)x)}] is e uq (a) x (b) sqrt(1-x^2) (c) 1/x...

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  20. The number of solutions of equation tan^(-1)2x+tan^(-1)3x=pi/4 is (...

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