document.write( "Question 79135: How can we prove sin(90° - A)= cos A? \n" ); document.write( "
Algebra.Com's Answer #56806 by Edwin McCravy(20060)\"\" \"About 
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document.write( "How can we prove sin(90° - A)= cos A?\r\n" );
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document.write( "We must use the identity:\r\n" );
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document.write( "sin(A - B) = sin(A)cos(B) - cos(A)sin(B)\r\n" );
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document.write( "However, there is already an A in your original \r\n" );
document.write( "problem, so to avoid confusion, first rewrite \r\n" );
document.write( "the above identity using different letters, say \r\n" );
document.write( "U and V. Then instead of the identity\r\n" );
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document.write( "sin(A - B) = sin(A)cos(B) - cos(A)sin(B)\r\n" );
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document.write( "after substituting U for A and V for B, we have\r\n" );
document.write( "the identity:\r\n" );
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document.write( "sin(U - V) = sin(U)cos(V) - cos(U)sin(V)\r\n" );
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document.write( "This is necessary to do when a formula you \r\n" );
document.write( "want to use contains a letter that is also\r\n" );
document.write( "contained in the expression you are wanting to \r\n" );
document.write( "use it in: \r\n" );
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document.write( "So to do your problem, \r\n" );
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document.write( "                                  sin(90° - A) = cos(A)\r\n" );
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document.write( "rewrite the left side using the identity\r\n" );
document.write( "sin(U - V) = sin(U)cos(V) - cos(U)sin(V)\r\n" );
document.write( "with U = 90° and V = A\r\n" );
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document.write( "               sin(90°)cos(A) - cos(90°)sin(A) = cos(A)\r\n" );
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document.write( "We use the fact that sin(90°) = 1 and cos(90°) = 0\r\n" );
document.write( "and substitute thes values:\r\n" );
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document.write( "                    (1)cos(A) - (0)sin(A) = cos(A)\r\n" );
document.write( "                       cos(A) -      0    = cos(A)      \r\n" );
document.write( "                                   cos(A) = cos(A)\r\n" );
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document.write( "Edwin
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