document.write( "Question 981787: verify the identity
\n" ); document.write( "cot(theta+pi/2)=-tan(theta) \n" ); document.write( "

Algebra.Com's Answer #602775 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "1. $\"cot%28theta%2Bpi%2F2%29\"$ = $\"cos%28theta%2Bpi%2F2%29%2Fsin%28theta%2Bpi%2F2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "2. $\"cos%28theta%2Bpi%2F2%29\"$ =     (apply the formula for cosines of the sum of angles, see the lesson Addition and subtraction formulas in this site, or any textbook on Trigonometry)\r
\n" ); document.write( "\n" ); document.write( "                         = $\"cos%28theta%29\"$ . $\"cos%28pi%2F2%29\"$ - $\"sin%28theta%29\"$ . $\"sin%28pi%2F2%29\"$ = $\"cos%28theta%29\"$ . $\"0%29\"$ - $\"sin%28theta%29\"$ . $\"1\"$ = $\"-sin%28theta%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "3. $\"sin%28theta%2Bpi%2F2%29\"$ =     (apply the formula for sines of the sum of angles, see the same lesson Addition and subtraction formulas in this site, or any textbook on Trigonometry)\r
\n" ); document.write( "\n" ); document.write( "                         = $\"sin%28theta%29\"$ . $\"cos%28pi%2F2%29\"$ + $\"cos%28theta%29\"$ . $\"sin%28pi%2F2%29\"$ = $\"sin%28theta%29\"$ . $\"0%29\"$ + $\"cos%28theta%29\"$ . $\"1\"$ = $\"cos%28theta%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Hence, $\"cot%28theta%2Bpi%2F2%29\"$ = $\"cos%28theta%2Bpi%2F2%29%2Fsin%28theta%2Bpi%2F2%29\"$ = $\"-sin%28theta%29%2Fcos%28theta%29\"$ = $\"-tan%28theta%29\"$ . \r
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\n" ); document.write( "\n" ); document.write( "Conclusion. The identity $\"cot%28theta%2Bpi%2F2%29\"$ = $\"-tan%28theta%29\"$ which was proposed you to verify, is true. \r
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