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Prove that 2tan^(-1)(cos e ctan^(-1)x-ta...

Prove that `2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x)=tan^(-1)x(x!=0)dot`

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The value of 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x) is equal to (a) cot^(-1)x (b) cot^(-1)1/x (c) tan^(-1)x (d) none of these

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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. If sin(sin^(-1)(1/5)+cos^(-1)x)=1, then find the value of x.

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  2. If sin^(-1)x=pi/5, for some x in (-1,1), then find the value of cos^(-...

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  3. Prove that 2tan^(-1)(cos e ctan^(-1)x-tancot^(-1)x)=tan^(-1)x(x!=0)dot

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  4. Find the value of sin^(-1)(sin7)+cos^(-1)(cos12)+tan^(-1){tan(-8)}+cot...

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  5. Solve sin^(-1)((14)/(|x|))+sin^(-1)((2sqrt(15))/(|x|))=pi/2

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  6. Find the minimum value of (sec^(-1)x)^2+("c o s e c"^(-1)x)^2

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  7. Find the value of lambda for which the three points with position vect...

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  8. Solve sin^(-1)xlt=cos^(-1)xdot

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  9. If 3tan^(-1)(1/(2+sqrt(3)))-tan^(-1)(1/x)=tan^(-1)(1/3), then x is equ...

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  10. The value 2tan^(-1)[sqrt((a-b)/(a+b))tan(theta/2)] is equal to cos^(-1...

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  11. If 1/2sin^(-1)[(3sin2theta)/(5+4cos2theta)]=tan^(-1)x ,t h e nx= (a...

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  12. If cot^(-1)(sqrt(cosalpha))-tan^(-1)(sqrt(cosalpha))=x , then sinx is ...

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  13. The value of tan^(-1)((xcostheta)/(1-xsintheta))-cot^(-1)((costheta)/(...

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  14. tan(pi/4+1/2cos^(-1)x)+tan(pi/4-1/2cos^(-1)x),x!=0, is equal to x (b)...

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  15. The sum of series sec^(-1) sqrt2 + sec^(-1).(sqrt10)/(3) + sec^(-1).(s...

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  16. The value of tan^(-1).(4)/(7) + tan^(-1).(4)/(19) + tan^(-1).(4)/(39) ...

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

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  18. If sin^(-1)((2a)/(1+a^2))+sin^(-1)((2b)/(1+b^2))=2tan^(-1)x , then x ...

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  19. If alpha=tan^(-1)((4x-4x^3)/(1-6x^2+x^4)),beta=2sin^(-1)((2x)/(1+x^2))...

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  20. Absolute value of sum of all integers in the domain of f(x)=cot^(-1)sq...

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