document.write( "Question 1204376: Find the sum
\n" ); document.write( "𝑆 = cos(𝑥 + 𝜃) + cos(2𝑥 + 3𝜃) + cos(3𝑥 + 5𝜃) + cos(4𝑥 + 7𝜃) + ⋯ + cos(40𝑥 + 79𝜃),
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Algebra.Com's Answer #840629 by Edwin McCravy(20065)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"S\"\"%22%22=%22%22\"\"sum%28%28k%2B1%29x%2B%282k%2B1%29theta%2Ck=0%2C40-1%29\"\r\n" );
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document.write( "We use this formula from \r\n" );
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document.write( "https://math.stackexchange.com/questions/17966/how-can-we-sum-up-sin-and-cos-series-when-the-angles-are-in-arithmetic-pro\r\n" );
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document.write( "\"sum%28cos%28a%2Bkd%29%2Ck=0%2Cn-1%29\"\"%22%22=%22%22\"\"expr%28sin%28n%2Aexpr%28d%2F2%29%29%2Fsin%28d%2F2%29%29\"\"%22%22%2A%22%22\"\"cos%28%282a%2B%28n-1%29d%29%2F2%29\"\r\n" );
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document.write( "We rewrite \r\n" );
document.write( "\"%28k%2B1%29x%2B%282k%2B1%29theta\"\"%22%22=%22%22\"\"kx%2Bx%2B2k%2Atheta%2Btheta\"\"%22%22=%22%22\"\"k%2Btheta%2Bkx%2B2k%2Atheta%29\"\"%22%22=%22%22\"\"%28x%2Btheta%29%2Bk%28x%2B2theta%29\"\r\n" );
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document.write( "So we substitute \"a=x%2Btheta\", \"d=x%2B2theta\", \"n=40\"\r\n" );
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document.write( "\"sum%28cos%28a%2Bkd%29%2Ck=0%2Cn-1%29\"\"%22%22=%22%22\"\"expr%28sin%28n%2Aexpr%28d%2F2%29%29%2Fsin%28d%2F2%29%29\"\"%22%22%2A%22%22\"\"cos%28%282a%2B%28n-1%29d%29%2F2%29\"\r\n" );
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document.write( "\"sum%28cos%28%28x%2Btheta%29%2Bk%28x%2B2theta%29%29%2Ck=0%2C40-1%29\"\"%22%22=%22%22\"\"expr%28sin%2840%2Aexpr%28%28x%2B2theta%29%2F2%29%29%2Fsin%28%28x%2B2theta%29%2F2%29%29\"\"%22%22%2A%22%22\"\"cos%28%282%28x%2Btheta%29%2B%2840-1%29%28x%2B2theta%29%29%2F2%29\"\"%22%22=%22%22\"\"expr%28sin%2840%2Aexpr%28%28x%2B2theta%29%2F2%29%29%2Fsin%28%28x%2B2theta%29%2F2%29%29\"\"%22%22%2A%22%22\"\"cos%28%282x%2B2theta%2B39x%2B78theta%29%2F2%29\"\r\n" );
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document.write( "Edwin
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