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

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

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We know that
`tan^(−1)sqrt(3)=π/3​`
`∴tan^(−1)sqrt(3)+cot^(−1)x=π/2​`
`⇒π/3​+cot^(−1)x=π/2​`
`⇒cot^(−1)x=π/2​−π/3​=π/6​`
`⇒x=cot(π/6)​=sqrt(3)​` ...
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RD SHARMA-INVERSE TRIGONOMETRIC FUNCTION-Solved Examples And Exercises
  1. What is the principal value of sin^(-1)(-(sqrt(2))/2)?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  16. Evaluate : cos(2cos^(-1)x+sin^(-1)x)a tx=1/5

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  17. Let f(x)=e^(cos^(-1){sin(x+pi/3)}) Then, f((8pi)/9)= (a)e^(5pi//18...

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  18. If u=cot^(-1)sqrt(tanalpha)-tan^(-1)sqrt(tanalpha),t h e ntan(pi/4- u/...

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

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  20. 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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