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anonymous

  • one year ago

Simplify the expression: Sin^2x-1/cos(-x)

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  1. SolomonZelman
    • one year ago
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    Have you seen the following identity? \(\large\color{black}{ \displaystyle \sin^2\theta+\cos^2\theta=1 }\)

  2. anonymous
    • one year ago
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    Yes

  3. SolomonZelman
    • one year ago
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    Subtract \(\sin^2\theta\) from both sides and tell me what you get.

  4. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle \sin^2\theta+\cos^2\theta =1 \ }\) \(\large\color{black}{ \displaystyle \sin^2\theta+\cos^2\theta \color{blue}{-\sin^2\theta }=1 \color{blue}{-\sin^2\theta } }\) \(\large\color{black}{ \displaystyle \cos^2\theta =1-\sin^2\theta }\)

  5. SolomonZelman
    • one year ago
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    So, based on the very last statement, you can now simplify your expression: \(\large\color{black}{ \displaystyle \frac{1-\sin^2x}{\cos x} =\frac{?}{\cos x} }\)

  6. SolomonZelman
    • one year ago
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    hello?

  7. anonymous
    • one year ago
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    Sinx?

  8. SolomonZelman
    • one year ago
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    We have concluded that: \(1-\sin^2\theta =\cos^2\theta\) correct?

  9. anonymous
    • one year ago
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    Yes so the ? Represents cos^2 theta?

  10. SolomonZelman
    • one year ago
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    Yes, therefore it comes out that: \(\large\color{black}{ \displaystyle \frac{1-\sin^2x}{\cos x} =\frac{\cos^2x}{\cos x} }\)

  11. SolomonZelman
    • one year ago
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    and THAT \(\Uparrow\) you can probably tell me how to simplify:D

  12. anonymous
    • one year ago
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    So the answer is cos x? :)

  13. SolomonZelman
    • one year ago
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    yes, just \(\cos x\).

  14. SolomonZelman
    • one year ago
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    Any questions?

  15. anonymous
    • one year ago
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    Thank you for your help! i understand it now :D

  16. SolomonZelman
    • one year ago
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    Yes, one more note: \(\color{red}{\cos(-\theta)=\cos(\theta)}\)

  17. SolomonZelman
    • one year ago
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    So, lets quicly recap everything once more, okay?

  18. SolomonZelman
    • one year ago
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    \(\large\color{black}{ \displaystyle \frac{1-\sin^2(x)}{\cos (-x)} = }\) \(\large\color{black}{ \displaystyle \frac{1-\sin^2(x)}{\cos (x)} = }\) \(\large\color{black}{ \displaystyle \frac{\cos^2(x)}{\cos (x)} = \cos(x) }\)

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