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Math Help - Pythagorean Identities to write expression as integer

  1. #1
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    Pythagorean Identities to write expression as integer

    Question is:
    Use Pythagorean identities to write the expression as an integer.

    Attached is the expression.

    How would you solve this one?
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  2. #2
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    Hi

    sec x is the hypotenuse of a right-angle triangle whose other sides are tan x and 1

    Therefore 1 + tan^2x = sec^2x

    Then tan^2x - sec^2x = -1

    List of trigonometric identities - Wikipedia, the free encyclopedia
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  3. #3
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    Quote Originally Posted by running-gag View Post
    Hi

    sec x is the hypotenuse of a right-angle triangle whose other sides are tan x and 1

    Therefore 1 + tan^2x = sec^2x

    Then tan^2x - sec^2x = -1

    List of trigonometric identities - Wikipedia, the free encyclopedia
    Thanks but how would you solve the above especially with the angle 4B?
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by mwok View Post
    Thanks but how would you solve the above especially with the angle 4B?
    Let x=4B...
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  5. #5
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    You are asked to write the expression as an integer

    Whatever x
    tan^2x - sec^2x = -1

    If you like whatever \beta
    tan^2(4\beta) - sec^2(4\beta) = -1

    EDIT : beaten by Chris !
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  6. #6
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    Quote Originally Posted by running-gag View Post
    You are asked to write the expression as an integer

    Whatever x
    tan^2x - sec^2x = -1

    If you like whatever \beta
    tan^2(4\beta) - sec^2(4\beta) = -1

    EDIT : beaten by Chris !

    I see but how do I solve it?
    Like tan^4(4B)....what does that come out to?
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  7. #7
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    Quote Originally Posted by mwok View Post
    I see but how do I solve it?
    Like tan^4(4B)....what does that come out to?
    What do you want to solve ?
    tan^2(4\beta) - sec^2(4\beta) is not an equation
    It is just an expression you are asked to write as an integer (which is -1)
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  8. #8
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    Okay, is this correct (different equation but same question).
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  9. #9
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    Not exactly
    csc^2\theta-cot^2\theta=1
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  10. #10
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    Quote Originally Posted by running-gag View Post
    Hi

    sec x is the hypotenuse of a right-angle triangle whose other sides are tan x and 1

    Therefore 1 + tan^2x = sec^2x

    Then tan^2x - sec^2x = -1

    List of trigonometric identities - Wikipedia, the free encyclopedia

    sorry to drudge up an old thread, but this problem is exactly the same problem i'm working on. I just don't get where -1 is coming from.

    if you substitute using the pythag. ident. the problem becomes

    tan^24B-1+tan^24B

    no?
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  11. #11
    Member purplec16's Avatar
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    Because tan^2 - sec^2 is = -1 it is the same as saying  1+ tan^2 4\beta= sec^2 4 \beta
    tan^2 4 \beta - sec^2 4 \beta = -1
    pretty much the 4 \beta doesnt matter it is jus like \theta
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