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Express tan^-1((1-sinx)/cosx) in the sim...

Express `tan^-1((1-sinx)/cosx)` in the simplest form.

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BODY BOOKS PUBLICATION-INVERSE TRIGONOMETRIC FUNCTIONS-EXERCISE
  1. Prove that sin^-1frac(4)(5)+sin^-1frac(5)(13)=sin^-1frac(63)(65)

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  2. Choose the correct answer from the bracket tan^-1((1-tanx)/(1+tanx)) e...

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  3. Express tan^-1((1-sinx)/cosx) in the simplest form.

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  4. Prove that tan^-1(1/2)-tan^-1(2/5)=tan^-1(1/12)

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  5. In which quadrants are the graph of cos^-1(x) lies,x in [-1,1]

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  6. If cos^-1x+cos^-1y=pi/3,then sin^-1x+sin^-1y=………..

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  7. if tan^-1x+tan^-1y=pi/4 then prove that x+y+xy=1

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  8. Find the values of the following tan frac(1)(2) [sin^(-1)((2x)/(1+x...

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  9. Evaluate tan^-1[2cos(2sin^-1(1/2)].

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  10. Prove that sin^-1(8/17)+sin^-1(3/5)=cos^-1(36/85)

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  11. The principal value of tan^-1(-1) is [pi/4,-pi/4,pi-pi/4,pi+pi/4]

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  12. If tan^-1 2+tan^-1 3=x, find x in radian

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  13. Find the principal value of sec^-1(-frac(2)(sqrt3))

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  14. Prove : tan^-1x=sec^-1sqrt(1+x^2).

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  15. Prove the following : tan^(-1)sqrtx=1/2 cos^(-1)((1-x)/(1+x)),x in[0,1...

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  16. Show that tan^-1(x/(sqrt(a^2-x^2)))=sin^-1(x/a)

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  17. Find the principal value of cos^-1(frac(sqrt3)(2))

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  18. In proving the result 3sin^-1x=sin^-1(3x-4x^3) Substitute x=

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  19. Prove that 3 sin ^(-1) x = sin^(-1) (3x - 4x^3), x in [-1/2,1/2]

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  20. Within the domain of definitions prove that sin^-1(-x)=-sin^-1x

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