Mathematics, 21.07.2019 10:00 angelearlyp9ynm9
Ireally need with these questions: use basic identities to find the simplified expression- 1. (cos^2 x + sin^2 x) / (cot^2 x - csc^2 x) 2. cosine θ^2 / sine θ^2 + csc θ sin θ explanations would be greatly appreciated
Answers: 2
![\bf sin^2(\theta)+cos^2(\theta)=1 \qquad \qquad cot(\theta)=\cfrac{cos(\theta )}{sin(\theta)} \qquad csc(\theta)=\cfrac{1}{sin(\theta)}\\\\ -------------------------------\\\\ \cfrac{cos^2(x)+sin^2(x)}{cot^2(x)-csc^2(x)}\implies \cfrac{1}{\frac{cos^2(x)}{sin^2(x)}-\frac{1}{sin^2(x)}}\implies \cfrac{1}{\frac{cos^2(x)-1}{sin^2(x)}} \\\\\\ \cfrac{1}{\frac{-[1-cos^2(x)]}{sin^2(x)}}\implies \cfrac{1}{\frac{-[\underline{sin^2(x)}]}{\underline{sin^2(x)}}}\implies \cfrac{1}{-1}\implies -1](/tpl/images/0115/2197/23eef.png)
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