document.write( "Question 1036529: Please help me solve this question\r
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Algebra.Com's Answer #651221 by ikleyn(52802)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "If alpha and beta are 2 positive acute angles satisfying alpha - beta = 15 degree and sin alpha = cos 2 beta then find value of alpha + beta
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document.write( "If \"sin%28alpha%29\" = \"cos%282%2Abeta%29\", then\r\n" );
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document.write( "\"sin%28alpha%29\" = \"sin%28pi%2F2-2%2Abeta%29\".\r\n" );
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document.write( "Due to constrains imposed on \"alpha\" and \"beta\", it implies that\r\n" );
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document.write( "\"alpha\" = \"pi%2F2+-+2%2Abeta\",   or\r\n" );
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document.write( "\"alpha+%2B+2%2Abeta\" = \"pi%2F2\".    (1)\r\n" );
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document.write( "From the condition, we also have the second equation \r\n" );
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document.write( "\"alpha+-+beta\" = \"pi%2F12\".      (2)     ( \"pi%2F12\" = 15 degs)\r\n" );
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document.write( "Distract equation (2) from (1) (both sides). You will get\r\n" );
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document.write( "\"3%2Abeta\" = \"pi%2F2+-+pi%2F12\" = \"%285pi%29%2F12\".\r\n" );
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document.write( "Hence, \"beta\" = \"%285pi%29%2F36\" = \"%285%2A180%29%2F36\" = 5*5 = 25 degs.\r\n" );
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document.write( "Then \"alpha\" = \"pi%2F2+-+2%2Abeta\" = \"pi%2F2+-+%2810pi%29%2F36\" = \"%28%2818-10%29%2Api%29%2F36\" = \"%288pi%29%2F36\" = \"2pi%2F9\" = 40 degs.\r\n" );
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document.write( "Answer.  \"alpha\" = \"2pi%2F9\" = 40 degs;  \"beta\" = \"%285pi%29%2F36\" = 25 degs.\r\n" );
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