1+cos^2 theta = 3 sin theta cos theta Rightar | vedclass

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Question

(C) Given the equation: $1 + \cos^2 	heta = 3 \sin 	heta \cos 	heta$. Divide both sides by $\cos^2 	heta$ (assuming $\cos 	heta 
eq 0$): $\sec^2

Vedclass · Accepted Answer

$n\pi + \frac{\pi}{4}, n\pi + 	an^{-1}(2); n \in \mathbb{Z}$

Vedclass · Answer

(C) Given the equation: $1 + \cos^2 	heta = 3 \sin 	heta \cos 	heta$. Divide both sides by $\cos^2 	heta$ (assuming $\cos 	heta 
eq 0$): $\sec^2 	heta + 1 = 3 	an 	heta$. Since $\sec^2 	heta = 1 + 	an^2 	heta$,we have: $(1 + 	an^2 	heta) + 1 = 3 	an 	heta$ $	an^2 	heta - 3 	an 	heta + 2 = 0$. Factoring the quadratic: $(	an 	heta - 1)(	an 	heta - 2) = 0$. This gives two cases: Case $1$: $	an 	heta = 1 \Rightarrow 	heta = n\pi + \frac{\pi}{4}$. Case $2$: $	an 	heta = 2 \Rightarrow 	heta = n\pi + 	an^{-1}(2)$. Thus,the solution is $n\pi + \frac{\pi}{4}, n\pi + 	an^{-1}(2); n \in \mathbb{Z}$.

$1+\cos^2 \theta = 3 \sin \theta \cos \theta \Rightarrow \theta = ?$

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