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

Prove that `tan(cot^(-1)x)=cot(tan^(-1)x)`

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To prove that \( \tan(\cot^{-1} x) = \cot(\tan^{-1} x) \), we will follow these steps: ### Step 1: Start with the Left-Hand Side (LHS) We begin with the left-hand side of the equation: \[ LHS = \tan(\cot^{-1} x) \] ...
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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Evaluate: sin^(-1)(sin((3pi)/5))

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  2. If (tan^(-1)x)^2+(cot^(-1)x)^2=(5pi^2)/8, then find xdot

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

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  4. Evaluate: tan{cos^(-1)(-7/(25))}

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

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  6. If -1lt=x , ylt=1 such that sin^(-1)x+sin^(-1)y=pi/2, find the value o...

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

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

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

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

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

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

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

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  15. 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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  16. The domain of cos^(-1)(x^2-4) is

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  17. In a A B C , , if C is a right angle, then tan^(-1)(a/(b+c))+tan^(-1)...

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  18. If 3sin^(-1)((2x)/(1+x^2))-4cos^(-1)((1-x^2)/(1+x^2))+2tan^(-1)((2x)/(...

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  19. Solve the following equations: sin[2cos^(-1)"{"cot"("2tan^(-1)x"}]...

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  20. Solve the equation of x:sin^(-1)x+sin^(-1)(1-x)=cos^(-1)x

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