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cos{cos^(- 1)((-sqrt(3))/2)+pi/6}...

`cos{cos^(- 1)((-sqrt(3))/2)+pi/6}`

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We have, `cos[cos^(-1)((-sqrt(3))/(2)) + (pi)/(6)] = cos[cos^(-1)(cos'(5pi)/(6))+(pi)/(6)] , [:' cos'(5pi)/(6) = (-sqrt(3))/(2)]`
`= cos((5pi)/(6) + (pi)/(6)), { :' cos^(-1) cos x = x, x in [0,pi]}`
`= cos((6pi)/(6))`
`= cos ((6pi)/(6))`
`= cos(pi) = - 1`
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NCERT EXEMPLAR-INVERSE TRIGONOMETRIC FUNCTIONS-Inverse Trigonometric Functions
  1. Evaluate: tan^(-1)(tan(5pi)/6)+cos^(-1){cos((13pi)/6)}

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  2. cos{cos^(- 1)((-sqrt(3))/2)+pi/6}

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  3. Prove that cot(pi/4-2cot^(- 1)3)=7

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  4. Find the value of tan^(-1)(-1/(sqrt(3)))+cot^(-1)((1)/(sqrt(3))) + ta...

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  5. Find the value of tan^(-1)(tan'(2pi)/(3)).

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  6. Show that 2tan^-1 (-3)=-pi/2+tan^-1(-4/3)

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  7. The number of real solutions of tan^(-1)sqrt(x(x+1))+sin^(-1)sqrt(x^2+...

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

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  9. If 2 tan^(-1)(costheta) = tan^(-1)(2 cosec theta), then show that the...

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

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  11. Solve the equation cos(tan^(-1)x) = sin(cot^(-1)'3/4).

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  12. Prove that tan^(-1)[(sqrt(1+x^2)+sqrt(1-x^2))/(sqrt(1+x^2)-sqrt(1-x^2...

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  13. Simplify each of the following: cos^(-1)(3/5cosx+4/5sinx) , where -(3p...

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  14. Prove that sin^(- 1)(8/17)+sin^(- 1)(3/5)=sin^(- 1)(77/85)

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  15. Show that sin^(-1)'5/13+cos^(-1)'3/5=tan^(-1)'63/16.

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  16. Prove: tan^(-1)(1/4)+tan^(-1)(2/9)=sin^(-1)(1/sqrt(5))

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  17. Find the value of 4 tan^-1 (1/5) - tan^-1 (1/239)

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  18. Show that: tan(1/2sin^(-1)3/4)=(4\ sqrt(-7))/3

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  19. If a1, a2,a3, ,an is an A.P. with common difference d , then prove th...

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  20. Which of the following of the principal value branch of cos^(-1)...

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