document.write( "Question 1023864: Find the value of without using calculator: sin^4 ( π/8)+sin^4 (3π/8)+sin^4 (5π/8)+sin^4 (7π/8) \n" ); document.write( "
Algebra.Com's Answer #639347 by robertb(5830)\"\" \"About 
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\"sin%5E4+%28pi%2F8%29%2Bsin%5E4+%283pi%2F8%29%2Bsin%5E4+%285pi%2F8%29%2Bsin%5E4+%287pi%2F8%29\"\r
\n" ); document.write( "\n" ); document.write( "=\"2sin%5E4+%28pi%2F8%29%2B2sin%5E4+%283pi%2F8%29\", \r
\n" ); document.write( "\n" ); document.write( "because \"sin+%28pi%2F8%29+=+sin+%287pi%2F8%29\" and \"sin%283pi%2F8%29+=+sin+%285pi%2F8%29\", since \"sin%28pi-x%29+=+sinx\"
\n" ); document.write( "Now because of the fact that \"sinx+=+cos%28pi%2F2-x%29\", the last expression is equal to\r
\n" ); document.write( "\n" ); document.write( " <----Equation (A)\r
\n" ); document.write( "\n" ); document.write( "Now \"cos2x+=+2cos%5E2%28x%29-1\" implies that\r
\n" ); document.write( "\n" ); document.write( "\"cos%282%2A%28pi%2F8%29%29+=+cos%28pi%2F4%29+=+sqrt%282%29%2F2+=+2cos%5E2%28pi%2F8%29-1\", hence\r
\n" ); document.write( "\n" ); document.write( "\"cos%5E2%28pi%2F8%29+=+%28sqrt%282%29+%2B2%29%2F4\"\r
\n" ); document.write( "\n" ); document.write( "==> \"cos%5E4%28pi%2F8%29+=+%283%2B2sqrt%282%29%29%2F8\"
\n" ); document.write( "Thus,
\n" ); document.write( "\r
\n" ); document.write( "\n" ); document.write( "after substitution into Equation A. \n" ); document.write( "
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