document.write( "Question 202605: prove sin 75 degrees – sin 15 degrees = cos 105 degrees + cos 15 degrees \n" ); document.write( "

Algebra.Com's Answer #152966 by jsmallt9(3758) $\"\"$ $\"About$

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Rewrite sin(75) and cos(105) as sin(90-15) and cos(90+15):
\n" ); document.write( "sin(90-15) - sin(15) = cos(90+15) + cos(15)

\n" ); document.write( "Using the sin(a-b) = sin(a)cos(b) - cos(a)sin(b) and cos(a+b) = cos(a)cos(b) - sin(a)sin(b) formulas we get:
\n" ); document.write( "sin(90)cos(15) - cos(90)sin(15) - sin(15) = cos(90)cos(15) - sin(90)sin(15) + cos(15)

\n" ); document.write( "sin(90) = 1
\n" ); document.write( "cos(90) = 0
\n" ); document.write( "Substituting these into our equation we get:
\n" ); document.write( "1*cos(15) - 0*sin(15) - sin(15) = 0*cos(15) - 1*sin(15) + cos(15)
\n" ); document.write( "Simplifying we get:
\n" ); document.write( "cos(15) - 0 - sin(15) = 0 - sin(15) + cos(15)
\n" ); document.write( "or
\n" ); document.write( "cos(15) - sin(15) = cos(15 - sin(15)
\n" ); document.write( " \n" ); document.write( "

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