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anonymous
 one year ago
Simplify the expression:
Sin^2x1/cos(x)
anonymous
 one year ago
Simplify the expression: Sin^2x1/cos(x)

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Have you seen the following identity? \(\large\color{black}{ \displaystyle \sin^2\theta+\cos^2\theta=1 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Subtract \(\sin^2\theta\) from both sides and tell me what you get.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0\(\large\color{black}{ \displaystyle \sin^2\theta+\cos^2\theta =1 \ }\) \(\large\color{black}{ \displaystyle \sin^2\theta+\cos^2\theta \color{blue}{\sin^2\theta }=1 \color{blue}{\sin^2\theta } }\) \(\large\color{black}{ \displaystyle \cos^2\theta =1\sin^2\theta }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0So, based on the very last statement, you can now simplify your expression: \(\large\color{black}{ \displaystyle \frac{1\sin^2x}{\cos x} =\frac{?}{\cos x} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0We have concluded that: \(1\sin^2\theta =\cos^2\theta\) correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yes so the ? Represents cos^2 theta?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Yes, therefore it comes out that: \(\large\color{black}{ \displaystyle \frac{1\sin^2x}{\cos x} =\frac{\cos^2x}{\cos x} }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0and THAT \(\Uparrow\) you can probably tell me how to simplify:D

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So the answer is cos x? :)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0yes, just \(\cos x\).

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thank you for your help! i understand it now :D

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0Yes, one more note: \(\color{red}{\cos(\theta)=\cos(\theta)}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0So, lets quicly recap everything once more, okay?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.0\(\large\color{black}{ \displaystyle \frac{1\sin^2(x)}{\cos (x)} = }\) \(\large\color{black}{ \displaystyle \frac{1\sin^2(x)}{\cos (x)} = }\) \(\large\color{black}{ \displaystyle \frac{\cos^2(x)}{\cos (x)} = \cos(x) }\)
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