TRIGONOMETRIC IDENTITIES
Fundamental Identities
tan๐ = sin๐
cos๐cot๐ = cos๐
sin๐
csc๐ = 1
sin๐ sec๐ = 1
cos๐ cot๐ = 1
tan๐
sin2๐+cos2๐ =1
1+ tan2๐ = sec2๐
1+ cot2๐ = csc2๐
Even-Odd Identities
sin(โ๐)= โsin ๐ csc(โ๐) = โcsc๐
cos(โ๐)=cos๐ sec( โ ๐) = sec ๐
tan(โ๐)= โtan๐ cot( โ๐) = โcot๐
Sum and Difference Formulas
sin(๐ผ+๐ฝ)= sin๐ผcos๐ฝ+cos๐ผsin๐ฝ
sin(๐ผโ๐ฝ)= sin๐ผcos๐ฝโcos๐ผsin๐ฝ
cos(๐ผ+๐ฝ)=cos๐ผcos๐ฝโ sin๐ผsin๐ฝ
cos(๐ผโ๐ฝ)=cos๐ผcos๐ฝ+ sin๐ผsin๐ฝ
tan(๐ผ+๐ฝ)=tan๐ผ+ tan๐ฝ
1โ tan๐ผtan๐ฝ
tan(๐ผโ๐ฝ)=tan๐ผโ tan๐ฝ
1+ tan๐ผtan๐ฝ
Cofunction Identities
cos(90ยฐ โ ๐) = sin ๐
sin(90ยฐ โ ๐) = cos ๐
tan(90ยฐ โ ๐) = cot ๐
Double-Angle Formulas
sin(2๐) = 2 sin ๐ cos ๐
cos(2๐) = cos2 ๐ โ sin2 ๐
= 2cos2๐ โ1
= 1 โ2sin2๐
tan(2๐)=2tan๐
1โ tan2๐
