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23-05-2023
Mathematics

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(a) Given that tan 2x + tan x = 0, show that tan x = 0 or tan2 x = 3. (b) (i) Given that + sin² θ = (5 + 3 cos θ) cos θ, show that cos θ = 3/4. (ii) Hence solve the equation 5+ sin² 2x = (5 + 3 cos 2x) cos 2x in the interval 0 < x < 21, giving your values of x in radians to three significant figures.

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