Given: sin(a+ b) = sin a cos b+ cos a sin b, we can figure out the following: sin(a? b) = sin(a+ (?b)) = sin a cos(?b) + cos a sin(?b) = sin a cos b+ cos a(? sin b) = sin a cos b? cos a sin b cos(a+b) = sin (pi 2 ? (a+ b) ) = sin ((pi 2 ? a ) ? b ) = sin (pi 2 ? a ) cos b?cos (pi 2 ? a ) sin b = cos a cos b?sin a sin b cos(a? b) = cos(a+ (?b)) = cos a cos(?b)? sin a sin(?b) = cos a cos b? sin a(? sin b) = cos a cos b+ sin a sin b tan(a+ b) = sin(a+ b) cos(a+ b) = sin a cos b+ cos a sin b cos a cos b? sin a sin b ? sec a sec b sec a sec b = sin a sec a+ sin b sec b 1? sin a sec a sin b sec b = tan a+ tan b 1? tan a tan b tan(a? b) = tan(a+ (?b)) = tan a+ tan(?b) 1? tan a tan(?b) = tan a+ (? tan b) 1? (? tan a tan b) = tan a? tan b 1 + tan a tan b

# Derivations of Trigonometry Formulas

Given: sin(a+ b) = sin a cos b+ cos a sin b, we can figure out the following: sin(a? b) = sin(a+ (?b)) = sin a cos(?b) + cos a sin(?b) = sin a cos b+ cos a(? sin b) = sin a cos b? cos a sin b cos(a+b) = sin (pi 2 ? (a+ b) ) = sin ((pi 2 ? a ) ? b ) = sin (pi 2 ? a ) cos b?cos (pi 2 ? a ) sin b = cos a cos b?sin a sin b cos(a? b) = cos(a+ (?b)) = cos a cos(?b)? sin a sin(?b) = cos a cos b? sin a(? sin b) = cos a cos b+ sin a sin b tan(a+ b) = sin(a+ b) cos(a+ b) = sin a cos b+ cos a sin b cos a cos b? sin a sin b ? sec a sec b sec a sec b = sin a sec a+ sin b sec b 1? sin a sec a sin b sec b = tan a+ tan b 1? tan a tan b tan(a? b) = tan(a+ (?b)) = tan a+ tan(?b) 1? tan a tan(?b) = tan a+ (? tan b) 1? (? tan a tan b) = tan a? tan b 1 + tan a tan b

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