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Write the value of cos((tan^(-1)x+cot^(-...

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

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We know that `tan^(-1)x+cot^(-1)x=frac{pi}{2}`
`=cos(pi/6)`
`=(sqrt 3)/2`
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. Write the value of tan^(-1)(1/x) for x<0 in terms of cot^(-1)(x) .

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

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

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

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

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

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

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

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

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

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

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

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

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

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  17. If alpha=tan^(-1)(t a n(5pi)/4)a n dbeta=tan^(-1)(-tan(2pi)/3),t h e n...

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  18. The number of real solutions of the equation sqrt(1+cos2x)=sqrt(2)sin^...

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  19. If x<0,\ y<0 such that x y=1 , then tan^(-1)x+tan^(-1)y equals pi/2 (b...

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  20. If u=cot^-1 sqrt(tanalpha)-tan^-1 sqrt(tan alpha), then tan(pi/4-u/2) ...

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