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Size:  325.1 KB Hi, I would like some help with question 9 please. Basically I managed to get the answer for the question but would like to know the other method to solve it.
    Attachment 565624565626 I don't get how part a could be used to solve b. Also for b I solved it by testing out which value of x for tan will be an exact number. I know that (60-45) will be the best option but how will u know as there are many different combinations that can give 15°. Thanks
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    (Original post by coconut64)
    Name:  146973096624236629119.jpg
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Size:  325.1 KB Hi, I would like some help with question 9 please. Basically I managed to get the answer for the question but would like to know the other method to solve it.
    Attachment 565624565626 I don't get how part a could be used to solve b. Also for b I solved it by testing out which value of x for tan will be an exact number. I know that (60-45) will be the best option but how will u know as there are many different combinations that can give 15°. Thanks
    Try plugging x=15 into the part a) identity.

    Post all your working if you get stuck.
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    (Original post by coconut64)
    Hi, I would like some help with question 9 please. Basically I managed to get the answer for the question but would like to know the other method to solve it.
    I don't get how part a could be used to solve b. Also for b I solved it by testing out which value of x for tan will be an exact number. I know that (60-45) will be the best option but how will u know as there are many different combinations that can give 15°. Thanks
    If you let x=15 degrees then you should get the left hand side in terms of tan(15) which is what you want, and the right hand side should be sin(30) [because it's 2x]. You should know that sin(30) is 1/2; if not, use triangles to work that out or your calculator. You can then get a quadratic in terms of tan(15). Complete the square on it and you should arrive to an answer with a \pm inside. Figure out why you disregard one of them and you should arrive to your answer.
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    (Original post by notnek)
    Try plugging x=15 into the part a) identity.

    Post all your working if you get stuck.
    Hi, sin(2*15)= 0.5 but it still doesn't ring any bell how this can be used to work out b. Thanks
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    (Original post by coconut64)
    Hi, sin(2*15)= 0.5 but it still doesn't ring any bell how this can be used to work out b. Thanks
    Then replace the right hand side with 0.5 and the left hand side should be in terms of tan(15). Solve for it.
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    (Original post by RDKGames)
    Then replace the right hand side with 0.5 and the left hand side should be in terms of tan(15). Solve for it.
    Hi, thanks for helping I managed to obtain 2+root3 and 2-root 3 following your instruction but I don't know which one to take out as both give me 0 why would it be 2-root 3?

    Also if I am not using part b to solve the question , how I will be able to know which value of x will give me an exact answer? For example tan(60) is root 3?

    Another question like this is finding the exact value of tan210. How will I know which two values to use to solve for this? There are many different combinations to get 210.
    Thanks
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    (Original post by coconut64)
    Hi, thanks for helping I managed to obtain 2+root3 and 2-root 3 following your instruction but I don't know which one to take out as both give me 0 why would it be 2-root 3?
    Will come back to this

    (Original post by coconut64)
    Also if I am not using part b to solve the question , how I will be able to know which value of x will give me an exact answer? For example tan(60) is root 3?
    You'd have to think about what values will give you tan(15) and work from there, but it is always better to use the part previously as it always links in to help in one way or another.

    (Original post by coconut64)
    Another question like this is finding the exact value of tan210. How will I know which two values to use to solve for this? There are many different combinations to get 210.
    You can use the double angle formulae and work with tan(180+30) where you know that tan(180) and tan(30) are rational. You should also aim to create the number using a combination of the two: 30,45,60,90,180 as you should know their trig rationals or it should be easy to work it out.
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    (Original post by coconut64)
    Hi, thanks for helping I managed to obtain 2+root3 and 2-root 3 following your instruction but I don't know which one to take out as both give me 0 why would it be 2-root 3?
    You can do a rough sketch of tan(x) and recognise that 2+\sqrt3 gives you a larger angle than it's conjugate. And rightfully so you can check on your calculator that it gives you 75 degrees rather than 15 which makes sense, a translation by 60 degrees. You can draw conclusions from there that this angle is too big in the range 0<degrees<90 therefore disregard it. I'm unsure if there is a more intuitive way of explaining this.
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    Don't think the above post is rigorous enough; note that 2 + \sqrt{3} &gt; 1 whilst 15^{\circ} is between 0\, and \frac{\pi}{4} where \tan is increasing, so 0 &lt; \tan 15^{\circ} &lt; 1.
 
 
 
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