document.write( "Question 714114: verify: tant+cost/1+sint=sec t
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Algebra.Com's Answer #438682 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I'll just do the first one:\r\n" );
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document.write( "tan(t) + \"cos%28t%29%2F%281%2Bsin%28t%29%29\" = sec(t)\r\n" );
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document.write( "Rationalize the denominator of the second term by\r\n" );
document.write( "multiplying it by \"%28conjugate_of_denominator%29%2F%28conjugate_of_denominator%29\"\"%22%22=%22%22\"\"%281-sin%28t%29%29%2F%281-sin%28t%29%29\"\r\n" );
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document.write( "tan(t) + \"cos%28t%29%2F%281%2Bsin%28t%29%29\"\"%22%22%2A%22%22\"\"%281-sin%28t%29%29%2F%281-sin%28t%29%29\"\r\n" );
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document.write( "tan(t) + \"%28cos%28t%29%281-sin%28t%29%29%29%2F%28%281%2Bsin%28t%29%29%281-sin%28t%29%29%29\"\r\n" );
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document.write( "tan(t) + \"%28cos%28t%29%281-sin%28t%29%29%29%2F%281-sin%5E2%28t%29%29\"\r\n" );
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document.write( "You know the identity \"sin%5E2%28theta%29%2Bcos%5E2%28theta%29=1\".  When it\r\n" );
document.write( "is solved like this \"cos%5E2%28theta%29=1-sin%5E2%28theta%29\" the right side\r\n" );
document.write( "is the same form as the denominator and so we can write \"1-sin%5E2%28t%29\"\r\n" );
document.write( "as \"cos%5E2%28t%29\"\r\n" );
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document.write( "tan(t) + \"%28cos%28t%29%281-sin%28t%29%29%29%2Fcos%5E2%28t%29\"\r\n" );
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document.write( "And we cancel the cos(t) on top into the cosē(t) in the bottom\r\n" );
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document.write( "tan(t) + \"%28cross%28cos%28t%29%29%281-sin%28t%29%29%29%2Fcos%5Ecross%282%29%28t%29\"  \r\n" );
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document.write( "tan(t) + \"%281-sin%28t%29%29%2Fcos%28t%29\"\r\n" );
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document.write( "Now we substitute \"sin%28t%29%2Fcos%28t%29\" for \"tan%28t%29\":\r\n" );
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document.write( "\"sin%28t%29%2Fcos%28t%29\"\"%22%22%2B%22%22\"\"%281-sin%28t%29%29%2Fcos%28t%29\"\r\n" );
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document.write( "Combine the fractions (they already have a common denominator):\r\n" );
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document.write( "\"%28sin%28t%29%2B1-sin%28t%29%29%2Fcos%28t%29\"\r\n" );
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document.write( "\"%28cross%28sin%28t%29%29%2B1-cross%28sin%28t%29%29%29%2Fcos%28t%29\"\r\n" );
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document.write( "\"1%2Fcos%28t%29\"\r\n" );
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document.write( "\"sec%28t%29\"\r\n" );
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document.write( "Edwin
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