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    There is a question which says
    "Prove cot 1/2A - tan 1/2A is identical to 2 cotA"
    Have been trying to solve it and it's gotten me nowhere.

    I've tried multiplying everything by tan but that gave me the wrong answer.
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    (Original post by B_Kazi)
    There is a question which says
    "Prove cot 1/2A - tan 1/2A is identical to 2 cotA"
    Have been trying to solve it and it's gotten me nowhere.

    I've tried multiplying everything by tan but that gave me the wrong answer.
    use the substitution t=tan1/2a and the formula tan(2a)= 2tana/1-tan^2a
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    First merge them, changing them to their sine and cosine versions so youll get (cosA/2 squared - sinA/2 squared)/(sinA/2 x cosA/2)

    Now the important part
    cos2A = cosA squared - sinA squared
    so, cosA = cosA/2 squared - sinA/2 squared (just divide all angles of the original double angle formula by 2)

    now we have the numerator fixed, so for the denominator

    sin2A = 2sinAcosA
    similarly, sinA =2sinA/2 x cosA/2
    divide the above equation by 2 to get sinA/2 x cosA/2 , which is (sinA)/2. or lets call it 0.5sinA

    thats the denominator

    Now, when we replace the numerator and denominator we have (cosA) / .5sinA
    cosA/sinA = cotA, diving that by .5 is same as multiplying it by 2 (since division essentially means multiplying with recriprocal)
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    late again ...
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    (Original post by N92991)
    First merge them, changing them to their sine and cosine versions so youll get (cosA/2 squared - sinA/2 squared)/(sinA/2 x cosA/2)

    Now the important part
    cos2A = cosA squared - sinA squared
    so, cosA = cosA/2 squared - sinA/2 squared (just divide all angles of the original double angle formula by 2)

    now we have the numerator fixed, so for the denominator

    sin2A = 2sinAcosA
    similarly, sinA =2sinA/2 x cosA/2
    divide the above equation by 2 to get sinA/2 x cosA/2 , which is (sinA)/2. or lets call it 0.5sinA

    thats the denominator

    Now, when we replace the numerator and denominator we have (cosA) / .5sinA
    cosA/sinA = cotA, diving that by .5 is same as multiplying it by 2 (since division essentially means multiplying with recriprocal)
    I would recommend using a different letter for your standard identities, rather than jumping from A and A/2 to 2A and A.
 
 
 
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