Question

find the value of theta if 2 - cos^2theta = 3 sin theta cos theta​

Answer 1

Answer:

Step-by-step explanation:

$2-cos^2\theta=3sin\theta\;cos\theta\\\\Squaring on both sides\\\\4+cos^4\theta-4cos^2\theta=9sin^2\theta\;cos^2\theta\\\\4+cos^4\theta-4cos^2\theta=9(1-cos^2\theta)cos^2\theta\\\\10cos^4\theta-13cos^2\theta+4=0\\\\10cos^4\theta-8cos^2\theta-5cos^2\theta+4=0\\\\2cos^2\theta\;(5cos^2\theta-4)-1(5cos^2\theta-4)=0\\\\(2cos^2\theta-1)(5cos^2\theta-4)=0\\\\cos\theta=\frac{1}{\sqrt{2}}\\\\cos\theta=-\frac{1}{\sqrt{2}}\\\\cos\theta=\frac{2}{\sqrt{5}}\\\\cos\theta=-\frac{2}{\sqrt{5}}$

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