Trig question

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  1. muh123's Avatar
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    Trig question
    Is Cosec^2(2x) - Cot^2(2x) = 1

    Does the double angle thing affect the identity ??
  2. raheem94's Avatar
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    Re: Trig question
    (Original post by muh123)
    Is Cosec^2(2x) - Cot^2(2x) = 1

    Does the double angle thing affect the identity ??
    The double angle shouldn't affect the identity,

     \displaystyle cosec^2(2x)-cot^2(2x)=1 is same as,  \displaystyle cosec^2\theta-cot^2\theta=1 , where  \displaystyle \theta =2x
  3. muh123's Avatar
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    Re: Trig question
    (Original post by raheem94)
    The double angle shouldn't affect the identity,

     \displaystyle cosec^2(2x)-cot^2(2x)=1 is same as,  \displaystyle cosec^2\theta-cot^2\theta=1 , where  \displaystyle \theta =2x
    Would it still be the same if it was 2 theta aswell ?
  4. raheem94's Avatar
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    Re: Trig question
    (Original post by muh123)
    Would it still be the same if it was 2 theta aswell ?
    Yes.

     \displaystyle cosec^2\theta-cot^2\theta = 1

    Now insert  \displaystyle \theta = 30^o

     \displaystyle cosec^230^o-cot^230^o=4-3=1

    You could have written it as,
     \displaystyle cosec^2(2\times 15)^o-cot^2(2\times 15)^o=4-3=1
     \displaystyle cosec^2(3\times 10)^o-cot^2(3\times 10)^o=4-3=1

    Still the answer would be same.
  5. reallytired's Avatar
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    Re: Trig question
    (Original post by raheem94)
    Yes.

     \displaystyle cosec^2\theta-cot^2\theta = 1

    Now insert  \displaystyle \theta = 30^o

     \displaystyle cosec^230^o-cot^230^o=4-3=1

    You could have written it as,
     \displaystyle cosec^2(2\times 15)^o-cot^2(2\times 15)^o=4-3=1
     \displaystyle cosec^2(3\times 10)^o-cot^2(3\times 10)^o=4-3=1

    Still the answer would be same.
    I was most impressed by your response to other questions but when you substituted a number to "prove" this, I was a little surprised.

    It's never possible to prove by numbers. Instead, use algebra!
  6. raheem94's Avatar
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    Re: Trig question
    (Original post by reallytired)
    I was most impressed by your response to other questions but when you substituted a number to "prove" this, I was a little surprised.

    It's never possible to prove by numbers. Instead, use algebra!
    The OP was stuck at a simple concept, so it was easier to prove him by numbers rather than prove.
    Last edited by raheem94; 06-04-2012 at 12:23.
  7. TenOfThem's Avatar
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    Re: Trig question
    (Original post by raheem94)
    The OP was stuck at a simple concept, so it was easier to DEMONSTRATE TO him by numbers rather than algebra.
    rather than prove
  8. raheem94's Avatar
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    Re: Trig question
    (Original post by TenOfThem)
    rather than prove
    Thanks for correcting.
  9. TenOfThem's Avatar
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    Re: Trig question
    (Original post by raheem94)
    Thanks for correcting.
    No problem ... after all ... your Post 2 showed the statement to be true for any substitution
  10. raheem94's Avatar
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    Re: Trig question
    (Original post by TenOfThem)
    No problem ... after all ... your Post 2 showed the statement to be true for any substitution
    I don't understand why reallytired disagreed with my posts, any reason?

    Was it wrong to try to explain by using numbers, i thought it will be easier for the OP to understand in this way.
  11. TenOfThem's Avatar
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    Re: Trig question
    By using numbers you only showed that the rule would work for theta=15 rather than a general proof

    Given the level of understanding of the OP this would, imo, have been enough to show him that it would work

    Reallytired seems to think a proof was required rather than a demonstration ... I guess that he was making the point that in a question that asks you to show or prove using a value to demonstrate would not be enough
    Last edited by TenOfThem; 06-04-2012 at 12:54.
  12. raheem94's Avatar
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    Re: Trig question
    (Original post by reallytired)
    I was most impressed by your response to other questions but when you substituted a number to "prove" this, I was a little surprised.

    It's never possible to prove by numbers. Instead, use algebra!
    (Original post by muh123)
    Is Cosec^2(2x) - Cot^2(2x) = 1

    Does the double angle thing affect the identity ??
    Here is the proof.

     \displaystyle cosec^2(2x)-cot^2(2x)=1 ,

     \displaystyle cosec^2(2x)-cot^2(2x) = \frac{1}{sin^2(2x)}-\frac{cos^2(2x)}{sin^2(2x)} = \frac{1-cos^2(2x)}{sin^2(2x)}

    From the identity,  \displaystyle sin^2(2x)+cos^2(2x)=1 \implies sin^2(2x)=1-cos^2(2x)

    So,  \displaystyle \frac{1-cos^2(2x)}{sin^2(2x)}= \frac{sin^2(2x)}{sin^2(2x)} = 1
    Last edited by raheem94; 07-04-2012 at 01:39.
  13. reallytired's Avatar
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    Re: Trig question
    (Original post by raheem94)
    Here is the proof.

     \displaystyle cosec^2(2x)-cot^2(2x)=1 ,

     \displaystyle cosec^2(2x)-cot^2(2x) = \frac{1}{sin^2(2x)}-\frac{cos^2(2x)}{sin^2(x)} = \frac{1-cos^2(2x)}{sin^2(2x)}

    From the identity,  \displaystyle sin^2(2x)+cos^2(2x)=1 \implies sin^2(2x)=1-cos^2(2x)

    So,  \displaystyle \frac{1-cos^2(2x)}{sin^2(2x)}= \frac{sin^2(2x)}{sin^2(2x)} = 1
    Well done (apart from a slight typo)! You intend to read maths at uni (I recall reading somewhere you are doing A-Levels ATM)?
    Last edited by reallytired; 07-04-2012 at 00:54.
  14. raheem94's Avatar
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    Re: Trig question
    (Original post by reallytired)
    Well done! You intend to read maths at uni (I recall reading somewhere you are doing A-Levels ATM)?
    No, i am going to do chemical engineering at uni.

    If you want to know more about the subjects i am doing, have a look at my profile.
  15. raheem94's Avatar
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    Re: Trig question
    (Original post by reallytired)
    Well done (apart from a slight typo)! You intend to read maths at uni (I recall reading somewhere you are doing A-Levels ATM)?
    Thanks for telling me about the typo, i have now corrected it.
  16. muh123's Avatar
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    Re: Trig question
    Yeah I knew how to do the proof sorry I was just being really lazy. I was just getting confused because I was thinking to much but many thanks to Raheem94 who cleared it up. it was like 3 in the morning and I was trying to do maths It doesn't work when I'm tired LOL
  17. raheem94's Avatar
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    Re: Trig question
    (Original post by muh123)
    Yeah I knew how to do the proof sorry I was just being really lazy. I was just getting confused because I was thinking to much but many thanks to Raheem94 who cleared it up. it was like 3 in the morning and I was trying to do maths It doesn't work when I'm tired LOL
    No problem but time isn't an excuse, i haven't slept from the last 23hours!
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