Verify an Identity

[nycmathguy]

Section 5.4

I need help with 87 and 89.

 

[MathLover1]

87.
cos(n*pi+theta)=(-1)^n*cos(theta) , n is an integer

when n is even number, n=2k, k element Z
then cos(n*pi+theta)=cos(2k*pi+theta)=1^(2k)*cos(theta)=cos(theta)

when n is odd number, n=2k+1, k element Z

then cos(n*pi+theta)=cos((2k+1)*pi+theta)=(-1^(2k)cos(theta)=- cos(theta)

cos(n*pi+theta)=(-1)^n*cos(theta)-> proven

89. is just as previous post

 

[nycmathguy]

87.
cos(n*pi+theta)=(-1)^n*cos(theta) , n is an integer

when n is even number, n=2k, k element Z
then cos(n*pi+theta)=cos(2k*pi+theta)=1^(2k)*cos(theta)=cos(theta)

then cos(n*pi+theta)=cos((2k+1)*pi+theta)=(-1^(2k)cos(theta)=- cos(theta)

cos(n*pi+theta)=(-1)^n*cos(theta)-> proven

89. is just as previous post

Moving forward, I will post questions for which Ron Larson and David Cohen (two different precalculus books) provide sample problems for. This makes a lot more sense than randomly selecting a bunch of problems for which there is nothing for me to use as a guide to answer similar problems. I am also wasting lots of time answering questions that are beyond my level of mathematics. So, skipping 89 here makes sense.