Verify the identity cosx cos (-x) - sinx sin (-x) = 1

(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)