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Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(...

Prove that: `cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-sinx)))=x/2,x in (0,pi/4)`

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RD SHARMA ENGLISH-INVERSE TRIGONOMETRIC FUNCTION-All Questions
  1. Express each of the following in the simplest form: tan^(-1){(cosx)/...

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  2. Prove that: (i)tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqr...

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  3. Prove that: cot^(-1)((sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

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  4. Prove that: tan^(-1){(sqrt(1+cosx)+sqrt(1-cosx))/(sqrt(1+cosx)-sqrt(1-...

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  5. Prove that: cot^(-1){(sqrt(1+sinx)+sqrt(1-sinx))/(sqrt(1+sinx)-sqrt(1-...

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  6. Write the following functions in the simplest form: (i)tan^(-1){x/(s...

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  7. Write the following functions in the simplest form: (i)sin^(-1){x/(s...

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  8. Prove that: tan^(-1){(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))}=pi/4...

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

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  10. Simplify each of the following: cos^(-1)(3/5cosx+4/5sinx) , where -(3p...

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  11. Simplify: sin^(-1)(5/(13)cosx+(12)/(13)sinx)

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  12. Simplify: sin^(-1)((sinx+cosx)/(sqrt(2))) where - π/4 < x < π/4

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  13. Simplify: cos^(-1)((sinx+cosx)/(sqrt(2))),π/4 < x <(5π)/4

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  14. Simplify each of the following: sin^(-1)((sinx+cosx)/(sqrt(2))),\ pi...

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  15. Evaluate the following: sin^(-1)(sin10) (ii) sin^(-1)(sin5)

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  16. Evaluate the following: cos^(-1)(cos10) (ii) tan^(-1){tan(-6)}

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  17. Evaluate each of the following: sin^(-1)(sin(pi/6)) (ii) sin^(-1)(si...

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  18. Evaluate each of the following: (i)sin^(-1)(sin((13pi)/7)) (ii) sin^...

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  19. Evaluate each of the following: sin^(-1)(sin3) (ii) sin^(-1)(sin4)

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  20. Evaluate each of the following: sin^(-1)(sin12) (ii) sin^(-1)(sin2)

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