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sin(cot^(-1)(tan(cos^(-1)x))) is equal t...

`sin(cot^(-1)(tan(cos^(-1)x)))` is equal to a) `x` b) `sqrt(1-x^2)` c) `1/x` d) none of these

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Put `cos^(−1)x=θ `
∴`x=cosθ`
∴`tanθ=sqrt(1−x^2)/x`
∴`tan(cos^(−1)x)=tanθ=sqrt(1−x^2)/x`
​​ ∴`cot^(−1)(tan(cos^(−1)))=cot^(−1)(sqrt(1−x^2)/x)=ϕ `(say) ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. For the principal values, evaluate the following: sin^(-1)(-(sqrt(3))...

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

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  3. sin(cot^(-1)(tan(cos^(-1)x))) is equal to a) x b) sqrt(1-x^2) c) 1/x d...

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  4. Write the value of tan^(-1){2sin(2cos^(-1)(sqrt(3))/2)}dot

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  5. Write the principal value of cos^(-1)(cos680^0)dot

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  6. What is the principal value of sin^(-1)(-(sqrt(2))/2)?

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  7. Write the principal value of cos^(-1)(cos(2pi)/3)+sin^(-1)(s in(2pi)/3...

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  8. If tan^(-1)(sqrt(3))+cot^(-1)x=pi/2,t h e nfin dxdot

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  9. If sin^(-1)(1/3)+cos^(-1)x=pi/2,then find x

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  10. Write the value of 2sin^(-1)\ 1/2+cos^(-1)((a-b)/(a+b))

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  11. Evaluate: sin^(-1)(s in(3pi)/5)

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  12. If (tan^(-1)x)^(2)+(cot^(-1)x)^(2)=(5 pi^(2))/(8), then the value of x...

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  13. Prove that tan(cot^(-1)x)=cot(tan^(-1)x)

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  14. Evaluate: (i) tan{cos^(-1)(-7/(25))} (ii) "c o s e c"{cot^(-1)(-(12)/...

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  15. Evaluate: sin{cos^(-1)(-(3)/5)+cot^(-1)(-5/(12))}

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  16. If -1lt=x , ylt=1 such that sin^(-1)x+sin^(-1)y=(2pi)/3, find the valu...

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  17. If tan^(-1)x+tan^(-1)y=(4pi)/5, find cot^(-1)x+cot^(-1)ydot

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  18. If tan^(-1)x-cot^(-1)x=tan^(-1)""1/(sqrt(3)) find the value of xdot

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  19. If sin(cos^(-1)(5/13)+sin^(-1)x)=1 find the value of xdot

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

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