Consider the equation a cos x + b sin x = c, where a, b and c are constants. a Show that the equation can be written in the form (a + c)t? - 2bt - (a - c) = 0, where t = tan x. b Show that the root(s) of the equation are real if c < a? + b². c Suppose that tan a and tan B are distinct real roots of the quadratic equation in part a. Prove that b tan (a + B) a

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