trig identities

sin(−𝜃) \=

− sin 𝜃

cos(−𝜃) \=

cos 𝜃

tan(−𝜃) \=

− tan 𝜃

csc(−𝜃) \=

− csc 𝜃

sec(−𝜃) \=

sec 𝜃

cot(−𝜃) \=

− cot 𝜃

tan 𝜃 \=

sin 𝜃/cos 𝜃

cot 𝜃 \=

cos 𝜃/sin 𝜃

sin^2 𝜃 + cos^2 𝜃 \=

1

tan^2 𝜃 + 1 \=

sec^2 𝜃

cot^2 𝜃 + 1 \=

csc^2 𝜃

sin 2𝜃

\= 2 sin 𝜃cos 𝜃

cos 2𝜃

\= cos^2 𝜃 − sin^2 𝜃

cos 2𝜃

\= 2 cos^2 𝜃 − 1

cos 2𝜃

\= 1 − 2 sin^2 𝜃

tan 2𝜃

\= 2 tan 𝜃/1 − tan2

sin(𝐴± 𝐵) \=

sin 𝐴 cos𝐵 ± cos 𝐴 sin 𝐵

cos(𝐴± 𝐵) \=

cos𝐴 cos 𝐵 ∓ sin 𝐴 sin𝐵

tan(𝐴 ± 𝐵) \=

(tan 𝐴 ± tan𝐵)/(1 ∓ tan𝐴 tanB)

sin 𝐴 sin 𝐵 \=

1/2 [cos(𝐴 − 𝐵) − cos(𝐴 + 𝐵)]

cos 𝐴 cos 𝐵 \=

1/2[cos(𝐴 + 𝐵) + cos(𝐴 − 𝐵)]

sin 𝐴 cos 𝐵 \=

1/2 [sin(𝐴 + 𝐵) + sin(𝐴 − 𝐵)]

cos 𝐴 sin 𝐵 \=

1/2 [sin(𝐴 + 𝐵) − sin(𝐴 − 𝐵)

sin𝐴 + sin𝐵 \=

2 sin[(𝐴+𝐵)/2] cos [(𝐴−𝐵)/2]

sin𝐴 − sin𝐵 \=

2 cos [(𝐴+𝐵)/2]sin[(𝐴−𝐵)/2]

cos𝐴 + cos𝐵 \=

2 cos [(𝐴+𝐵)/2] cos [(𝐴−𝐵)/2]

cos𝐴 − cos𝐵 \=

−2 sin [(𝐴+𝐵)/2]sin[(𝐴− 𝐵)/2]