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    deduce that tan22.5 is a root of the equation t2+2t-1=0, and hence find the exact value of tan22.5. I did the first part of the question but can not work out how to find the exact value. i'm guessing it's something to do with tan(2A) formula and tan45=1 but have no idea how to go about it! please help
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    (Original post by emma201295)
    deduce that tan22.5 is a root of the equation t2+2t-1=0, and hence find the exact value of tan22.5. I did the first part of the question but can not work out how to find the exact value. i'm guessing it's something to do with tan(2A) formula and tan45=1 but have no idea how to go about it! please help
    Since you've worked out that tan22.5 is one of the roots. Work out the exact value of the roots using the quadratic formula. You'll get two values, and one you should be able to discard because it can't be tan 22.5
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    (Original post by emma201295)
    deduce that tan22.5 is a root of the equation t2+2t-1=0, and hence find the exact value of tan22.5. I did the first part of the question but can not work out how to find the exact value. i'm guessing it's something to do with tan(2A) formula and tan45=1 but have no idea how to go about it! please help
    If A = 22.5, 2A = 45 so tan(2A) = 1.

    Use your formula for tan(2A) in terms of tanA to get a quadratic in tanA and then solve, rejecting one possible solution as suggested.
 
 
 
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