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Answers
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Step-by-step explanation:
Prove:
cos
(
A
)
1
−
sin
(
A
)
=
1
+
sin
(
A
)
cos
(
A
)
Multiply the left side by 1 in the form of
cos
(
A
)
cos
(
A
)
:
cos
2
(
A
)
cos
(
A
)
(
1
−
sin
(
A
)
)
=
1
+
sin
(
A
)
cos
(
A
)
Substitute
cos
2
(
A
)
=
1
−
sin
2
(
A
)
1
−
sin
2
(
A
)
cos
(
A
)
(
1
−
sin
(
A
)
)
=
1
+
sin
(
A
)
cos
(
A
)
Factor the numerator:
(
1
−
sin
(
A
)
)
(
1
+
sin
(
A
)
)
cos
(
A
)
(
1
−
sin
(
A
)
)
=
1
+
sin
(
A
)
cos
(
A
)
Cancel the common factor:
(
1
−
sin
(
A
)
)
(
1
+
sin
(
A
)
)
cos
(
A
)
(
1
−
sin
(
A
)
)
=
1
+
sin
(
A
)
cos
(
A
)
Write without the cancelled factors:
1
+
sin
(
A
)
cos
(
A
)
=
1
+
sin
(
A
)
cos
(
A
)
Q.E.D.
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