cos A sin A + 1-tan A 1-cot A Prove that: =sin A + cos A
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Answer: See the pdf above
We want to prove that:
cos
A
1
−
tan
A
+
sin
A
1
−
cot
A
≡
cos
A
+
sin
A
If we manipulate the LHS we have:
L
H
S
=
cos
A
1
−
tan
A
+
sin
A
1
−
cot
A
=
cos
A
1
−
sin
A
cos
A
+
sin
A
1
−
cos
A
sin
A
=
cos
A
cos
A
−
sin
A
cos
A
+
sin
A
sin
A
−
cos
A
sin
A
=
cos
2
A
cos
A
−
sin
A
+
sin
2
A
sin
A
−
cos
A
=
cos
2
A
cos
A
−
sin
A
−
sin
2
A
cos
A
−
sin
A
=
cos
2
A
−
sin
2
A
cos
A
−
sin
A
=
(
cos
A
+
sin
A
)
(
cos
A
−
sin
A
)
cos
A
−
sin
A
=
cos
A
+
sin
A
QED
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