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baddinlol

  • 2 years ago

Find the real values of x for which the equation is valid.

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  1. baddinlol
    • 2 years ago
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    \[2\cos (x)=\sqrt{3}\cot (x)\]

  2. Rosh007
    • 2 years ago
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    can you right cot (x) in terms of sin and cos

  3. Rosh007
    • 2 years ago
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    ***write nor right

  4. baddinlol
    • 2 years ago
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    I wrote cot(x)=cos(x)/sin(x)

  5. baddinlol
    • 2 years ago
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    And then i cancelled the cos(x)

  6. Rosh007
    • 2 years ago
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    yup good

  7. baddinlol
    • 2 years ago
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    And i was left with sin(x) = sqrt(3)/2

  8. Rosh007
    • 2 years ago
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    now can you write what answer you got

  9. baddinlol
    • 2 years ago
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    I then thought i can get infinite answers....

  10. baddinlol
    • 2 years ago
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    So i wrote pi/3 and 2pi/3

  11. baddinlol
    • 2 years ago
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    I think there are more solutions but i dont know how to writee them

  12. Rosh007
    • 2 years ago
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    ..... ok can you tell me what is th sin invers of \[\sin^{-1}( \frac{ \sqrt{3} }{ 2 })\]

  13. baddinlol
    • 2 years ago
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    It is pi/3 and 2pi/3 between 0 and 2pi

  14. Rosh007
    • 2 years ago
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    How you got 2pi/3

  15. baddinlol
    • 2 years ago
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    I did pi - pi/3 because sin is also positive in that quadrant

  16. Rosh007
    • 2 years ago
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    yes exactly.. so when we find inverse if get more values we take the lesser value usually.. for example 7pi/3 is also giving same answer but by using the concept above answer will b what?

  17. baddinlol
    • 2 years ago
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    is it pi/3?

  18. Rosh007
    • 2 years ago
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    yup it is

  19. baddinlol
    • 2 years ago
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    But i need to state all the values for it

  20. baddinlol
    • 2 years ago
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    so i need to write, pi/3, 2pi/3, 7pi/3, 8pi/3, 13pi/3, 14pi/3 .......

  21. baddinlol
    • 2 years ago
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    How can i write this as a general solution

  22. Rosh007
    • 2 years ago
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    ok.. first take a look at pi/3 and 7pi/3 what can you find

  23. Rosh007
    • 2 years ago
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    any similarity?.. or relation... (clue can you relate with multiple of 2pi

  24. baddinlol
    • 2 years ago
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    Oo i think i found it

  25. baddinlol
    • 2 years ago
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    Is it pi/3 + 2kpi

  26. baddinlol
    • 2 years ago
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    and 2pi/3 + 2kpi

  27. Rosh007
    • 2 years ago
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    exactly.. ther you go... what is k...( no need to tll if you ar pretty sure)

  28. baddinlol
    • 2 years ago
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    And one more thing

  29. baddinlol
    • 2 years ago
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    Will i also need to evaluate cos(x)=0?

  30. Rosh007
    • 2 years ago
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    ??? not clear... cab you make it more clear?is it another question?

  31. Rosh007
    • 2 years ago
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    ** can

  32. Rosh007
    • 2 years ago
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    if it is another qustion your answer is (2k+1)pi/2

  33. baddinlol
    • 2 years ago
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    No same one

  34. baddinlol
    • 2 years ago
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    wouldn't 2cos(x) = sqrt(3)cot(x) if cos(x) = 0 also

  35. Rosh007
    • 2 years ago
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    am I clear?

  36. Rosh007
    • 2 years ago
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    ok...... asuming a fuction itself is zero may not lad you to corrct ansewr... also... here the cos (x) cancels each other (ofcourse before assuming it zero) hence assuming cos (x) = 0 is wrong..

  37. Rosh007
    • 2 years ago
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    **lead you to correct answer

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