Difference between revisions of "005 Sample Final A, Question 14"
Jump to navigation
Jump to search
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)}}
(Created page with "''' Question ''' Prove the following identity, <br> <center><math>\frac{1-\sin(\theta)}{\cos(\theta)}=\frac{\cos(\theta)}{1+\sin(\theta)}</math></center> {| class="mw-collap...") |
|||
| Line 10: | Line 10: | ||
|Answers: | |Answers: | ||
|- | |- | ||
| − | | | + | |2) You can multiply <math>1 - \sin(\theta)</math> by <math>\frac{1 + \sin(\theta)}{1 + \sin(\theta)} </math> |
|} | |} | ||
Latest revision as of 09:54, 2 June 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: |
| 2) 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: |
|---|
| 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)}} |