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Trigonometry Question: Double of Half Angle Formula

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Use a double or half angle formula to solve the equation in the interval [0, 2x].
a) tan (x/2) - sin(x) = 0
b) tan(x) + cot(x) = 4sin(2x)

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Solution Preview

tan x/2 = sin x
sin x/2/ cos x/2 = 2 sin x/2 cos x/2

sin x/2 = 0 or 1/ cos x/2 = 2 cos x/2
cos^2 (x/2) = ½

Case 1.
sin x/2 = 0
x/2 = npie
x = +/- 2npie => x = 0, 2pie (these are the solutions within the given interval of x)

Case 2.
cos x/2 = 1/?2
x/2 = pie/4 and 2pie - pie/4 = 7pie/4 are solutions. (1st and 4th quadrants)
x/2 = pie/4 + 2npie and ...

Solution Summary

In this solution we solve two trigonometry questions using a double or half angle formula.

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