Answer:
(identity has been verified)
Step-by-step explanation:
Verify the following identity:
cos(x) cos(-x) - sin(x) sin(-x) = 1
Hint: | Cosine is an even function.
Use the identity cos(-x) = cos(x):
cos(x) cos(x) - sin(-x) sin(x) = ^?1
Hint: | Sine is an odd function.
Use the identity sin(-x) = -sin(x):
cos(x) cos(x) - -sin(x) sin(x) = ^?1
Hint: | Evaluate cos(x) cos(x).
cos(x) cos(x) = cos(x)^2:
cos(x)^2 - ( - sin(x) sin(x)) = ^?1
Hint: | Evaluate -(-sin(x)) sin(x).
-(-sin(x)) sin(x) = sin(x)^2:
cos(x)^2 + sin(x)^2 = ^?1
Hint: | Use the Pythagorean identity on cos(x)^2 + sin(x)^2.
Substitute cos(x)^2 + sin(x)^2 = 1:
1 = ^?1
Hint: | Come to a conclusion.
The left hand side and right hand side are identical:
Answer: (identity has been verified)
