Difference between revisions of "005 Sample Final A, Question 14"
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Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1-\sin(\theta)}{\cos(\theta)}=\frac{\cos(\theta)}{1+\sin(\theta)}}
Kayla Murray (talk | contribs) |
Kayla Murray (talk | contribs) |
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| − | | | + | |We start with the left hand side. We have <math>\frac{1-\sin(\theta)}{\cos(\theta)}=\frac{1-\sin(\theta)}{\cos(\theta)}\Bigg(\frac{1+\sin(\theta)}{1+\sin(\theta)}\Bigg)</math>. |
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! Step 2: | ! Step 2: | ||
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| − | | | + | | Simplifying, we get <math>\frac{1-\sin(\theta)}{\cos(\theta)}=\frac{1-\sin^2(\theta)}{\cos(\theta)(1+\sin(\theta))}</math>. |
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! Step 3: | ! Step 3: | ||
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| − | | | + | | Since <math>1-\sin^2(\theta)=\cos^2(\theta)</math>, we have |
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| − | | | + | |<math>\frac{1-\sin(\theta)}{\cos(\theta)}=\frac{\cos^2(\theta)}{\cos(\theta)(1+\sin(\theta))}=\frac{\cos(\theta)}{1+\sin(\theta)}</math> |
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Revision as of 13:14, 20 May 2015
Question Prove the following identity,
| Step 1: |
|---|
| We start with the left hand side. We have Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1-\sin(\theta)}{\cos(\theta)}=\frac{1-\sin(\theta)}{\cos(\theta)}\Bigg(\frac{1+\sin(\theta)}{1+\sin(\theta)}\Bigg)} . |
| Step 2: |
|---|
| Simplifying, we get Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1-\sin(\theta)}{\cos(\theta)}=\frac{1-\sin^2(\theta)}{\cos(\theta)(1+\sin(\theta))}} . |
| Step 3: |
|---|
| Since Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1-\sin^2(\theta)=\cos^2(\theta)} , we have |
| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1-\sin(\theta)}{\cos(\theta)}=\frac{\cos^2(\theta)}{\cos(\theta)(1+\sin(\theta))}=\frac{\cos(\theta)}{1+\sin(\theta)}} |