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logynklode

  • 2 years ago

cot x sec4x = cot x + 2 tan x + tan3x

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  1. mahmit2012
    • 2 years ago
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    Is this equation or identity?

  2. logynklode
    • 2 years ago
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    Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

  3. ganeshie8
    • 2 years ago
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    \(\cot x \sec^4 x = \cot x + 2 \tan x + \tan^3 x \)

  4. ganeshie8
    • 2 years ago
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    its like above ?

  5. logynklode
    • 2 years ago
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    huh?

  6. ganeshie8
    • 2 years ago
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    *the equation u seeing in ur assessment sheet, is it like the one ive posted above ?

  7. logynklode
    • 2 years ago
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    its tan cubed x at the end other then that yes

  8. ganeshie8
    • 2 years ago
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    ok thnks :) pick the side that has more terms, and do SOMETHING and try getting to the other side

  9. ganeshie8
    • 2 years ago
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    here, the right side has more terms, right ?

  10. logynklode
    • 2 years ago
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    what? the irght side has more terms yeah

  11. ganeshie8
    • 2 years ago
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    ya so we start with that side, and work, and prove that it equals left side.

  12. logynklode
    • 2 years ago
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    okay

  13. ganeshie8
    • 2 years ago
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    \(\cot x + 2\tan x + \tan^3 x\) \(\frac{1}{\tan x} + 2\tan x + \tan^3 x\) \(\frac{1+ 2\tan^2 x + \tan^4 x}{\tan x}\) \(\frac{1+ \tan^2 x + \tan^2x + \tan^4 x}{\tan x}\) \(\frac{\sec^2 x + \tan^2x + \tan^4 x}{\tan x}\) \(\frac{\sec^2 x + \tan^2x(1 + \tan^2 x)}{\tan x}\) \(\frac{\sec^2 x + \tan^2x(\sec^2 x)}{\tan x}\) \(\frac{\sec^2 x(1 + \tan^2x)}{\tan x}\) \(\frac{\sec^2 x(\sec^2 x)}{\tan x}\) \(\frac{\sec^4 x}{\tan x}\) \(\cot x\sec^4 x\) = LEFT HAND SIDE

  14. ganeshie8
    • 2 years ago
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    thats the complete solution; see if it makes sense

  15. jishan
    • 2 years ago
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    good solve ganeshie.,...........

  16. rubypearl11
    • one year ago
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    How did you get rid of the tan^4x? @ganeshie8?

  17. mayaal
    • 5 months ago
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    @ganeshie8 i dont understand ur solution

  18. ganeshie8
    • 5 months ago
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    hmm which line ?

  19. mayaal
    • 5 months ago
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    the 3rd line from the end.

  20. ganeshie8
    • 5 months ago
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    \[\large \frac{\sec^2 x + \tan^2x(\sec^2 x)}{\tan x}\]

  21. ganeshie8
    • 5 months ago
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    you're fine, till this line ?

  22. mayaal
    • 5 months ago
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    yes

  23. ganeshie8
    • 5 months ago
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    good, next factor out `sec^2x` from both terms, you get : \[\large \frac{\sec^2 x(1 + \tan^2x)}{\tan x}\]

  24. ganeshie8
    • 5 months ago
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    still fine ?

  25. mayaal
    • 5 months ago
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    oh,ok.so u factored out the sec^2x from the whole numerator?

  26. ganeshie8
    • 5 months ago
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    exactly !

  27. mayaal
    • 5 months ago
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    great!thnku very much @ganeshie8

  28. ganeshie8
    • 5 months ago
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    np :)

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