Instead, we have to use logical steps to show that one side of the equation can be transformed to the other side of the equation. Sometimes, we will work separately on each side, till they meet in the middle.
ESSENTIAL IDENTITIES:
sin(x)=1csc(x)
cos(x)=1sec(x)
tan(x)=1cot(x)
sec(x)=1cos(x)
csc(x)=1sin(x)
cot(x)=1tan(x)
tan(x)=sin(x)cos(x)
sin(−x)=−sin(x)
cos(−x)=cos(x)
tan(−x)=−tan(x)
Pythagorean Identitiessin2(x)+cos2(x)=1
1+tan2(x)=sec2(x)
1+cot2(x)=csc2(x)
Sum and Difference Formulassin(a+b)=sin(a)cos(b)+cos(a)sin(b)
sin(a−b)=sin(a)cos(b)−cos(a)sin(b)
cos(a+b)=cos(a)cos(b)−sin(a)sin(b)
cos(a−b)=cos(a)cos(b)+sin(a)sin(b)
tan(a+b)=tan(a)+tan(b)1−tan(a)tan(b)
tan(a−b)=tan(a)−tan(b)1+tan(a)tan(b)
sin(x)+sin(y)=2sin(x+y2)cos(x−y2)
sin(x)−sin(y)=2cos(x+y2)sin(x−y2)
cos(x)+cos(y)=2cos(x+y2)cos(x−y2)
cos(x)−cos(y)=−2sin(x+y2)sin(x−y2)
Double Angle Formulassin(2x)=2sin(x)cos(x)
cos(2x)=cos2(x)−sin2(x)=1−2sin2(x)=2cos2(x)−1
Half Angle Formulassin(x2)=±1−cos(x)2−−−−−−√
cos(x2)=±1+cos(x)2−−−−−−√
tan(x2)=±1−cos(x)1+cos(x)−−−−−−√=1−cos(x)sin(x)=sin(x)1+cos(x)
Trigonometric Productssin(x)cos(y)=sin(x+y)+sin(x−y)2
cos(x)cos(y)=cos(x+y)+cos(x−y)2
sin(x)sin(y)=cos(x−y)−cos(x+y)2
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