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Question Number 134872 by bemath last updated on 08/Mar/21

$$-------------$$ Trygonometri What is the value of cosA if cosA+3sinA=2?\n

Answered by EDWIN88 last updated on 08/Mar/21

$$\mathrm{We}\mathrm{have}\sin \mathrm{A}=\pm \sqrt{1-\cos {}^2\mathrm{A}}$$ $$\mathrm{then}3\sin \mathrm{A}=2-\cos \mathrm{A},\mathrm{square}\mathrm{to}\mathrm{get}$$ $$9\sin {}^2\mathrm{A}={(2-\cos \mathrm{A})}^2$$ $$9-9\cos {}^2\mathrm{A}=\cos {}^2\mathrm{A}-4\cos \mathrm{A}+4$$ $$10\cos {}^2\mathrm{A}-4\cos \mathrm{A}-5=0$$ $$\cos \mathrm{A}=\frac{4\pm \sqrt{16+4.50}}{20}=\frac{4\pm 2\sqrt{54}}{20}$$ $$\cos \mathrm{A}=\frac{2\pm 3\sqrt{6}}{10}$$

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