document.write( "Question 946318: Verify that the following is an identity: tan(theta+pi/2)= -cot theta \n" ); document.write( "
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\n" ); document.write( "(1) tan(x+90) = -cot(x)
\n" ); document.write( "Use the trig identity
\n" ); document.write( "(2) tan(x) = sin(x)/cos(x) to get
\n" ); document.write( "(3) tan(x+90) = sin(x+90)/cos(x+90)
\n" ); document.write( "Now use the trig identities
\n" ); document.write( "(4) sin(a+b) = sin(a)cos(b) + cos(a)sin(b) and
\n" ); document.write( "(5) cos(a+b) = cos(a)cos(b) - sin(a)sin(b)
\n" ); document.write( "in (3) to get
\n" ); document.write( "(6) tan(x+90) = (sin(x)cos(90) + cos(x)sin(90))/(cos(x)cos(90) - sin(x)sin(90))
\n" ); document.write( "Now using
\n" ); document.write( "(7) cos(90) = 0
\n" ); document.write( "(8) sin(90) = 1
\n" ); document.write( "in (6) we get
\n" ); document.write( "(9) tan(x+90) = (sin(x)*0 + cos(x)*1)/(cos(x)*0 - sin(x)*1) or
\n" ); document.write( "(10) tan(x+90) = cos(x)/(-sin(x)) or
\n" ); document.write( "(11) tan(x+90) = -cos(x)/sin(x)
\n" ); document.write( "Use the trig identity
\n" ); document.write( "(12) cot(a) = cos(a)/sin(a) (11) becomes
\n" ); document.write( "(13) tan(x+90) = -cot(x) QED \n" ); document.write( "
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