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Prove that: cosec(tan^(-1)("cos"(cot^(-1...

Prove that: `cosec(tan^(-1)("cos"(cot^(-1)("sec"(sin^(-1)a)))))=sqrt(3-a^2),` where `a in [0,1]`

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Here `x = cosec (tan^(-1) (cos (cot^(-1) (sec (sin^(-1) a)))))`
`=cosec (tan^(-1) (cos (cot^(-1) ((1)/(sqrt(1 - a^(2)))))))`
`= cosec(tan^(-1) ((1)/(sqrt(2 - a^(2)))))`
`= sqrt(3 - a^(2))`
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CENGAGE PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-All Questions
  1. Express sin^(-1).(sqrtx)/(sqrt(x + a)) as a function of tan^(-1)

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  2. If tan(cos^(-1) x) = sin (cot^(-1)(1/2)), then find the value of x

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  3. Prove that: cosec(tan^(-1)("cos"(cot^(-1)("sec"(sin^(-1)a)))))=sqrt(3-...

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  4. Prove that sin cot^(-1) tan cos^(-1) x = sin cosec^(-1) cot tan^(-1) x...

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  5. tan^(- 1)((sqrt(1+a^2x^2)-1)/(a x)) where x!=0, is equal to

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  6. Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

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  7. Prove that tan^(-1)((1)/(sqrt(x^(2) -1))) = (pi)/(2) - sec^(-1) x, x g...

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  8. Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/...

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  9. If x lt 0, the prove that cos^(-1) ((1 + x)/(sqrt(2(1 + x^(2))))) = (p...

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  10. Find the value of tan^(-1) (-tan((13pi)/(8)))+ cot^(-1) (-cot((19pi)/(...

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  11. The value of tan{(cos^(- 1)(-2/7)-pi/2)] is

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  12. If tan^-1(1/y)=-pi+cot^-1 y, where y=x^2-3x+2, then find the value of ...

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

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  14. solve the equation cot^-1 x + tan^-1 3 = pi/2

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  15. Solve 2 cos^(-1) x + sin^(-1) x = (2pi)/(3)

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  16. Prove that sin^(-1) cos (sin^(-1) x) + cos^(-1) x = (pi)/(2), |x| le 1

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  17. If sin^(-1)x+sin^(-1)y=(2pi)/3 and cos^(-1)x-cos^(-1)y=-pi/3 then the ...

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

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  19. Solve sec^(-1) x gt cosec^(-1) x

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  20. Solve tan^(-1) x gt cot^(-1) x

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