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Question-189897




Question Number 189897 by Mingma last updated on 23/Mar/23
Answered by mr W last updated on 24/Mar/23
a^2 =cos^2  x+4 sin^2  x  b^2 =4 cos^2  x+1+4 cos^2  x=8 cos^2  x+1  c^2 =4+sin^2  x+4 sin^2  x=5 sin^2  x+4  a^2 +b^2 =c^2   9 cos^2  x+4 sin^2  x+1=5 sin^2  x+4  5 sin^2  x=3  sin x=(√(3/5)) ✓
$${a}^{\mathrm{2}} =\mathrm{cos}^{\mathrm{2}} \:{x}+\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:{x} \\ $$$${b}^{\mathrm{2}} =\mathrm{4}\:\mathrm{cos}^{\mathrm{2}} \:{x}+\mathrm{1}+\mathrm{4}\:\mathrm{cos}^{\mathrm{2}} \:{x}=\mathrm{8}\:\mathrm{cos}^{\mathrm{2}} \:{x}+\mathrm{1} \\ $$$${c}^{\mathrm{2}} =\mathrm{4}+\mathrm{sin}^{\mathrm{2}} \:{x}+\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:{x}=\mathrm{5}\:\mathrm{sin}^{\mathrm{2}} \:{x}+\mathrm{4} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} ={c}^{\mathrm{2}} \\ $$$$\mathrm{9}\:\mathrm{cos}^{\mathrm{2}} \:{x}+\mathrm{4}\:\mathrm{sin}^{\mathrm{2}} \:{x}+\mathrm{1}=\mathrm{5}\:\mathrm{sin}^{\mathrm{2}} \:{x}+\mathrm{4} \\ $$$$\mathrm{5}\:\mathrm{sin}^{\mathrm{2}} \:{x}=\mathrm{3} \\ $$$$\mathrm{sin}\:{x}=\sqrt{\frac{\mathrm{3}}{\mathrm{5}}}\:\checkmark \\ $$
Commented by Rupesh123 last updated on 24/Mar/23
Excellent!

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