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    I don't understand how to solve this question:

    By writing the following equations as quadratics in tanx/2, solve, in the interval 0<x<360:
    i) sinx+2cosx=1
    ii) 3cosx-4sinx=2

    The answers and working are here: https://9d7fc71c7b4ac6b796d66d68d061...3lyYXM/CH7.pdf (page 73 exC Q7 part b)
    however I don't understand the jump between each step and also the initial part after tanx/2 was substituted for t. Could anyone please explain?
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    (Original post by louderthanlove)
    I don't understand how to solve this question:

    By writing the following equations as quadratics in tanx/2, solve, in the interval 0<x<360:
    i) sinx+2cosx=1
    ii) 3cosx-4sinx=2

    The answers and working are here: https://9d7fc71c7b4ac6b796d66d68d061...3lyYXM/CH7.pdf (page 73 exC Q7 part b)
    however I don't understand the jump between each step and also the initial part after tanx/2 was substituted for t. Could anyone please explain?
    Using the formulae derived in part a) and subbing that in to the equation given gives the first step.
    Algebraic manipulation gives each of the following steps, multiplying both sides by 1+t^2 and so forth. The t is essentially just short-hand.
    This boils down to a quadratic in t, but recalling that t=\tan \left( \dfrac{\theta}{2} \right) gives the solutions for \dfrac{\theta}{2} and hence for \theta.
 
 
 
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