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Prove that tan^(-1){x/(a+sqrt(a^2-x^2))...

Prove that `tan^(-1){x/(a+sqrt(a^2-x^2))}=1/2sin^(-1)x/a ,-a lt x lt a`

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CENGAGE-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Prove that cos^(-1)((1-x^(2n))/(1+x^(2n)))=2tan^(-1)x^n ,0 lt x lt oo

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  2. Prove that cos^(-1){(1+x)/2}=(cos^(-1)x)/2

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  3. Prove that tan^(-1){x/(a+sqrt(a^2-x^2))}=1/2sin^(-1)x/a ,-a lt x lt a

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  4. Prove that: cos e c(tan^(-1)("cos"(cot^(-1)("sec"(sin^(-1)a)))))=sqrt(...

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  5. If x lt 0, then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))

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  6. If cos^(-1)x-cos^(-1)y/2=alpha,t h e n4x^2-4x ycosalpha+y^2 is equal t...

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  7. If sin^(-1)x+sin^(-1)y+sin^(-1)z=pi,t h e nx^4+y^2+z^4+4x^2y^2z^2=K(x^...

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  8. If f(x)=sin^(-1)((sqrt(3))/2x-1/2sqrt(1-x^2)),-1/2lt=xlt=1,t h e nf(x)...

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  9. Let |[tan^(-1)x,tan^(-1)2x,tan^(-1)3x],[tan^(-1)3x,tan^(-1)x,tan^(-1)2...

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  10. If x1=2tan^(-1)((1+x)/(1-x)),x2=sin^(-1)((1-x^2)/(1+x^2)) , where x in...

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

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  12. If the equation x^3+b x^2+c x+1=0,(bltc), has only one real root alpha...

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  13. The value of sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)] is equal to

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  14. Which of the following is the solution set of the equation 2cos^(-1)x=...

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  15. The number of solution of equation sin^(-1)x+nsin^(-1)(1-x)=(mpi)/2,w ...

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  16. Number of solutions of equation sin(cos^(-1)(tan(sec^(-1)x)))=sqrt(1+x...

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  17. Let f:[0,4pi]->[0,pi] be defined by f(x)=cos^-1(cos x). The number ...

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  18. The principal value of sin^(-1)(sin((2pi)/3)) is (a)-(2pi)/3 (b) (2pi...

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  19. If sec^(-1)x=cos e c^(-1)y , then find the value of cos^(-1)1/x+cos^(-...

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  20. If alpha=sin^(-1)(cos(sin^(-1)x))a n dbeta=cos^(-1)("sin"(cos^(-1)x)),...

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