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)}}
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| + | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" | ||
| + | ! Foundations: | ||
| + | |- | ||
| + | |1) What can you multiply <math>1- \sin(\theta)</math> by to obtain a formula that is equivalent to something involving <math>\cos</math>? | ||
| + | |- | ||
| + | |Answers: | ||
| + | |- | ||
| + | |1) You can multiply <math>1 - \sin(\theta)</math> by <math>\frac{1 + \sin(\theta)}{\1 + \sin(\theta)}</math> | ||
| + | |} | ||
{| class="mw-collapsible mw-collapsed" style = "text-align:left;" | {| class="mw-collapsible mw-collapsed" style = "text-align:left;" | ||
Latest revision as of 21:10, 21 May 2015
Question Prove the following identity,
| Foundations: |
|---|
| 1) What can you multiply 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(\theta)} by to obtain a formula that is equivalent to something involving 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 \cos} ? |
| Answers: |
| 1) You can multiply 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(\theta)} by 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)}{\1 + \sin(\theta)}} |
| Step 1: |
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| 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: |
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| 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: |
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| 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)}} |