prove that cos (π+theta) =-cos theta
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Answer:
While a different answer mentions the unit circle, another way of arriving at the solution is to use the identity
cos
(
α
+
β
)
=
cos
(
α
)
cos
(
β
)
−
sin
(
α
)
sin
(
β
)
along with the fact that
cos
(
−
α
)
=
cos
(
α
)
With that, we have
cos
(
π
−
θ
)
=
cos
(
π
+
(
−
θ
)
)
=
cos
(
π
)
cos
(
−
θ
)
−
sin
(
π
)
sin
(
−
θ
)
=
(
−
1
)
cos
(
−
θ
)
−
0
sin
(
−
θ
)
=
−
cos
(
−
θ
)
−
0
=
−
cos
(
−
θ
)
=
−
cos
(
θ
)
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