Consider the trigonometric equation $2\sin^2{x} = 1 + \cos{x}$. Write this equation in the form \(

Question

Consider the trigonometric equation $2\sin^2{x} = 1 + \cos{x}$. Write this equation in the form $f(x) = 0$, where $f(x) = a\cos^2{x} + b\cos{x} + c$, and $a, b, c \in \mathbb{Z}$. Factorise $f(x)$. Solve $f(x) = 0$ for $0^{\circ} \leq x \leq 360^{\circ}$.

Accepted Answer

(a) $f(x)=2\cos^2x+\cos x-1$ (b) $f(x)=(2\cos x-1)(\cos x+1)$ (c) $x=60^\circ,180^\circ,300^\circ$

Trigonometry - Trigonometric Equations

Trigonometry - Trigonometric Equations

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