Let's first simplify the expression by using the difference of squares formula:
(cos215° - sin215°)·(cos215° + sin215°)= cos^2(215°) - sin^2(215°)
Next, we can use the trigonometric identities to rewrite cos^2(215°) and sin^2(215°):
cos(2θ) = cos^2(θ) - sin^2(θ)sin(2θ) = 2sin(θ)cos(θ)
Thus, we have:
cos(2(215°)) = cos(430°)sin(2(215°)) = sin(430°)
Since the cosine function is periodic with a period of 360 degrees, we can simplify further:
cos(430°) = cos(430° - 360°) = cos(70°)sin(430°) = sin(430° - 360°) = sin(70°)
Therefore, the expression simplifies to:
cos^2(215°) - sin^2(215°)= cos(70°) - sin(70°)
Therefore, (cos215° - sin215°)·(cos215° + sin215°) simplifies to cos(70°) - sin(70°).
Let's first simplify the expression by using the difference of squares formula:
(cos215° - sin215°)·(cos215° + sin215°)
= cos^2(215°) - sin^2(215°)
Next, we can use the trigonometric identities to rewrite cos^2(215°) and sin^2(215°):
cos(2θ) = cos^2(θ) - sin^2(θ)
sin(2θ) = 2sin(θ)cos(θ)
Thus, we have:
cos(2(215°)) = cos(430°)
sin(2(215°)) = sin(430°)
Since the cosine function is periodic with a period of 360 degrees, we can simplify further:
cos(430°) = cos(430° - 360°) = cos(70°)
sin(430°) = sin(430° - 360°) = sin(70°)
Therefore, the expression simplifies to:
cos^2(215°) - sin^2(215°)
= cos(70°) - sin(70°)
Therefore, (cos215° - sin215°)·(cos215° + sin215°) simplifies to cos(70°) - sin(70°).