# Trigonometric Ratios for Compound Angles

- cos(
*A*â€“*B*) = cos*A*cos*B*+ sin*A*sin*B* - cos(
*A*+*B*) = cos*A*cos*B*â€“ sin*A*sin*B* - sin(
*A*â€“*B*) = sin*A*cos*B*â€“ cos*A*sin*B* - sin(
*A*+*B*) = sin*A*cos*B*+ cos*A*sin*B* - tan(
*A*+*B*) = - tan(
*A*â€“*B*) = - sin(
*A*+*B*) sin (*A*â€“*B*) = sin^{2}*A*â€“ sin^{2}*B = cos*^{2}*B*â€“ cos^{2}*A* - cos(
*A*+*B*) cos(*A*â€“*B*) = cos^{2}*A*â€“ sin^{2}*B = cos*^{2}*B*â€“ sin^{2}*A* - tan(
*A*+*B*+*C*) =

# Range of *f*(*Î¸*) = *a* cos *Î¸* + *b* sin *Î¸*

Now

*f*(*Î¸*) =*a*cos*Î¸*+*b*sin*Î¸*=

=

=

=

which has range