document.write( "Question 1187797: Consider angles x and y such that 0 <_ y <_ x <_ pi/2 and sin(x+y) = 0.9 while sin(x-y) = 0.6. What is the value of (sin x + cos x)(sin y + cos y)? \n" ); document.write( "

Algebra.Com's Answer #818829 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "Consider angles x and y such that 0 <_ y <_ x <_ pi/2 and sin(x+y) = 0.9 while sin(x-y) = 0.6.
\n" ); document.write( "What is the value of (sin x + cos x)(sin y + cos y)?
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\n" ); document.write( "\n" ); document.write( " Actually, it is a joke problem of Trigonometry, and (as it should be for any joke problem),\r
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document.write( "  (sin x + cos x)(sin y + cos y) = sin(x)*sin(y) + cos(x)*sin(y) + sin(x)*cos(y) + cos(x)*cos(y) = \r\n" );
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document.write( "        (regroup the terms)\r\n" );
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document.write( "= ( cos(x)*sin(y) + sin(x)*cos(y) ) + ( cos(x)*cos(y) + sin(x)*sin(y) ) = sin(x+y) + cos(x-y).\r\n" );
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document.write( "Now calculate  cos(x-y) =  =  =  =  = 0.8.\r\n" );
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document.write( "    Notice that the angle (x-y)  is in QI,  where  cosine is positive,\r\n" );
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document.write( "    so we select and use the positive value of the square root . . . \r\n" );
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document.write( "At this point, we just have everything to continue and complete our calculations\r\n" );
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document.write( "    (sin x + cos x)(sin y + cos y) = sin(x+y) + cos(x-y) = 0.9 + 0.8 = 1.7.     ANSWER\r\n" );
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