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    Hi, I'm given a question like below :
    F= Int(1/(7-5sinx)). There is a hint of using u=tan(x/2)
    I'm not too sure how to do this. I feel like I'm missing something. Help please?
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    have you tried rearraging tan(x/2) in terms of tan(x)? or sinx in terms of sin(x/2)?
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    This is a well known type of substitution (actually known as the "t substitution").

    Can you use geometry to find sinx in terms of u?
    Also dx/du in terms of u ?
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    (Original post by reaped)
    have you tried rearraging tan(x/2) in terms of tan(x)? or sinx in terms of sin(x/2)?
    I have tried both but I'm not sure where I'm going with it... In the case of rearranging tan(x/2) in terms of tan(x)... Once I get there, do I just change that to sinx/cosx?
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    sorry i don't think rearranging tan(x/2) is the right approach to the question. Try to rearrange sinx using the double angle formula
    Spoiler:
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     \sin {x} = 2\sin {\frac {x}{2}}\cos {\frac {x}{2}}
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    (Original post by reaped)
    sorry i don't think tan(x/2) is the right approach to the question. Try to rearrange sinx using the double angle formula
    Once using the double angle formulae, how does that lead to any form of tanx or tan(x/2)? And the substitution of u=tan(x/2)?
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    sinx = 2sin(x/2)*cos(x/2)

    Use a right-angled triangle showing tan(x/2) = u/1 (i.e. opposite over adjacent) to find sin(x/2) and cos(x/2) in terms of u, and hence sinx...
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    Community Assistant
    (Original post by lalyala)
    Hi, I'm given a question like below :
    F= Int(1/(7-5sinx)). There is a hint of using u=tan(x/2)
    I'm not too sure how to do this. I feel like I'm missing something. Help please?
    If you private message me with an email address, I will send you a powerpoint on t subs.
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    (Original post by lalyala)
    Once using the double angle formulae, how does that lead to any form of tanx or tan(x/2)? And the substitution of u=tan(x/2)?
    using a little bit of manipulation you can deduce that  \sin {x} = 2\tan {\frac {x}{2}} (\cos {\frac {x}{2}})^{2}
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    also this talk about t subs sounds like it could be a much easier way to solve the problem rather that trying from first principles. I'm on the edexcel board so I haven't learnt anything about them (yet).
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    Just looked up the t-substitution thing and it should work. Thanks so much everyone!
 
 
 
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