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    a) Given x is obtuse and sin x = 5/13, find the value of cos 2x
    b) Show that sec⁡x - cos⁡x ≡ tanxsinx

    Need help on both of them
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    (Original post by emx_eco)
    a) Given x is obtuse and sin x = 5/13, find the value of cos 2x
    b) Show that sec⁡x - cos⁡x ≡ tanxsinx

    Need help on both of them
    How far have you got?
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    (Original post by Muttley79)
    How far have you got?
    For a) I have cosx = -12/13 (not sure about this answer)

    For b) I've tried different ways but I'm just not getting anywhere
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    For a start with: cos x = √1-sin^2 x
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    (Original post by wiseguy99)
    For a start with: cos x = √1-sin^2 x
    What do you mean?
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    For the second par replace tan(x) with a function of sin and cos
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    (Original post by wiseguy99)
    For the second par replace tan(x) with a function of sin and cos
    Okay, I'm really confused now . So for part a) did you get cosx = -12/13 or not?
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    (Original post by emx_eco)
    a) Given x is obtuse and sin x = 5/13, find the value of cos 2x
    b) Show that sec⁡x - cos⁡x ≡ tanxsinx

    Need help on both of them
    What have you done?

    A tip for the first one: Think about Pythagorean Triples. Do those numbers ring a bell? Then note that x is obtuse, so is cos x positive or negative? Once you know sin x and cos x you can find cos2x.

    For questions like the second one, if in doubt, write the everything solely in terms of sin then cos, then experiment with multiplying through with things.
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    (Original post by TheMindGarage)
    What have you done?

    A tip for the first one: Think about Pythagorean Triples. Do those numbers ring a bell? Then note that x is obtuse, so is cos x positive or negative? Once you know sin x and cos x you can find cos2x.

    For questions like the second one, if in doubt, write the everything solely in terms of sin then cos, then experiment with multiplying through with things.

    For part a) I drew out a triangle to work out that cosx = -12/13. Is this what you got?
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    (Original post by emx_eco)
    a) Given x is obtuse and sin x = 5/13, find the value of cos 2x
    b) Show that sec⁡x - cos⁡x ≡ tanxsinx

    Need help on both of them
    For part 1
    use the formula sinx=root ((1-cos2x)/2)
    For part 2
    since secx is 1/cosx substitute it there then add, you should get sin^2x/cosx after placing sin^2x in place of 1-cos^2x.
    then split. that's it
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    (Original post by emx_eco)
    For part a) I drew out a triangle to work out that cosx = -12/13. Is this what you got?
    This is correct. Now you need to find cos(2x).

    You could have done this question with an identity linking cos(2x) and sin. Then you wouldn't have had to find cos(x).
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    (Original post by Notnek)
    For a) you could use an identity or a triangle. Have you done questions like this before?

    You should start by using an identity to rewrite cos(2x). Please post all your working.
    Everybody's been telling me different things. I'm just totally confused now . Can some just what they've done step be step?
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    (Original post by Notnek)
    This is correct. Now you need to find cos(2x).

    You could have done this question with an identity linking cos(2x) and sin. Then you wouldn't have had to find cos(x).
    Okay, I understand this part now, thank you

    So how would you do part b)?
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    (Original post by emx_eco)
    Everybody's been telling me different things. I'm just totally confused now . Can some just what they've done step be step?
    That's because there are different ways to do it. The quickest way is to write cos(2x) in terms of sin(x) which is an identity you should know.
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    (Original post by emx_eco)
    For part a) I drew out a triangle to work out that cosx = -12/13. Is this what you got?
    Yes. That's right. Alternatively you could have used sin^2 x + cos^2 x = 1.
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    (Original post by emx_eco)
    Okay, I understand this part now, thank you

    So how would you do part b)?
    You need to somehow turn two terms (the left-hand-side) into one term and normally the best way to do this is to combine fractions.

    So you can write sec(x) = 1/cos(x) and then subtract the fractions i.e. put them over a common denominator. Try this and post your working if you get stuck.
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    (Original post by themindgarage)
    yes. That's right. Alternatively you could have used sin^2 x + cos^2 x = 1.
    thank you everyone i just figured out both the questions. I feel so dumb rn i dunno how i didn't see it before. :d thanks for all your help, reps for you all xxx
 
 
 
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