document.write( "Question 1142951: cos15 - cos75 =\r
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\n" ); document.write( "\n" ); document.write( "How do you solve this? The material I learned does not include radians so, I have no clue where to start. What is the formula for this problem? \n" ); document.write( "
Algebra.Com's Answer #763690 by ikleyn(52879)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "cos(15°) = cos(45°-30°)       (1) \r\n" );
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document.write( "    use the basic formula of Trigonometry  cos(a-b) = cos(a)*cos(b) + sin(a)*sin(b).\r\n" );
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document.write( "    Continue line (1) in this way\r\n" );
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document.write( "cos(15°) = cos(45°-30°) = cos(45°)*cos(30°) + sin(45°)*sin(30°) = \"%28sqrt%282%29%2F2%29%2A%28sqrt%283%29%2F2%29\" + \"%28sqrt%282%29%2F2%29%2A%281%2F2%29\".    (2)\r\n" );
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document.write( "cos(75°) = cos(45°-30°)       (3) \r\n" );
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document.write( "    use the basic formula of Trigonometry  cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b).\r\n" );
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document.write( "    Continue line (3) in this way\r\n" );
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document.write( "cos(75°) = cos(45°+30°) = cos(45°)*cos(30°) - sin(45°)*sin(30°) = \"%28sqrt%282%29%2F2%29%2A%28sqrt%283%29%2F2%29\" - \"%28sqrt%282%29%2F2%29%2A%281%2F2%29\".    (4)\r\n" );
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document.write( "Now, subtract (4) from (2).   You will get\r\n" );
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document.write( "    cos(15°) - cos(75°) = \"sqrt%282%29%2F2\".\r\n" );
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document.write( "Now, you should know that 360° = \"2%2Api\".\r\n" );
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document.write( "Hence,\r\n" );
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document.write( "\"pi%2F8\" = \"360%5Eo%29%2F16\" = 22.5°;\r\n" );
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document.write( "\"pi%2F3\" = \"360%5Eo%2F6\" = 60°;\r\n" );
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document.write( "\"pi%2F4\" = \"360o%2F8\" = 45°;\r\n" );
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document.write( "\"pi%2F2\" = \"360%5Eo%2F4\" = 90°.\r\n" );
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document.write( "Next,  \"sqrt%282%29%2F2\" = sin(45°).\r\n" );
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document.write( "Hence, the answer to the problem's question is  the third line  \"sin%28pi%2F4%29\".\r\n" );
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