document.write( "Question 1170519: Hi, may i know how to solve this question? thank you~
\n" ); document.write( "The first three terms of an arithmetic progression are 2 sin x, 3 cos x and (sin x + 2 cos x) respectively, where x is an acute angle. Show that tan x = 4/3. Hence, find the sum of the first twenty terms of the progression. [ Use tan x = 4/3 for sin x and cos x ] \n" ); document.write( "

Algebra.Com's Answer #795403 by ikleyn(52797) $\"\"$ $\"About$

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document.write( "The characteristic property that three numbers ,  and   form an Arithmetic progression is this equality  \r\n" );
document.write( "     -  =  - \r\n" );
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document.write( "In our case, it means that\r\n" );
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document.write( "    3cos(x) - 2sin(x) = (sin(x) + 2cos(x)) - 3cos(x).\r\n" );
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document.write( "Simplify it\r\n" );
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document.write( "    3cos(x) - 2 cos(x) + 3cos(x) = sin(x) + 2sin(x)\r\n" );
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document.write( "    4cos(x)                      = 3sin(x).\r\n" );
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document.write( "Divide both sides by cos(x).  You will get\r\n" );
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document.write( "                     = ,   or\r\n" );
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document.write( "        tan(x)         = .\r\n" );
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document.write( "So, the first statement is proved.\r\n" );
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document.write( "--------\r\n" );
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document.write( "Next, if tan(x) =   and the angle x is acute,  then there is only one possibility:\r\n" );
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document.write( "    the angle x is in QI, and  sin(x) =  = 0.8,  cos(x) =  = 0.6.\r\n" );
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document.write( "In this case,  the 1st term of the AP is  2*0.8 = 1.6;  \r\n" );
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document.write( "               the 2nd term of the AP is  3*0.6 = 1.8  and\r\n" );
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document.write( "               the common difference is   1.8 - 1.6 = 0.2.\r\n" );
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document.write( "               Then the 20th term is 1.6+19*0.2 = 5.4  and\r\n" );
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document.write( "                    the sum of the first 20 terms is   = 70.\r\n" );
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