Question
1) Use the cofunction identites to evaluate the expression without the aid of a calculator.
cos^2 18 degrees + cos^2 72 degrees.
cos^2 18 degrees + cos^2 72 degrees.
Answers
Abby
Error
Reiny
The cofunction identities that are useful here are
cos(90-x) = sinx and
sin(90-x) = cosx
and the fact that cos(A-B) = cosAcosB + sinAsinB
so cos^2 72 = (cos72)(cos72) = (sin18)(sin18)
then your
cos^2 18 degrees + cos^2 72 degrees
= cos18cos18 + sin18sin18
= cos(18-18)
= cos 0
= 1
cos(90-x) = sinx and
sin(90-x) = cosx
and the fact that cos(A-B) = cosAcosB + sinAsinB
so cos^2 72 = (cos72)(cos72) = (sin18)(sin18)
then your
cos^2 18 degrees + cos^2 72 degrees
= cos18cos18 + sin18sin18
= cos(18-18)
= cos 0
= 1