Prove that Cos A/1-tan A + sin^2/sin A - cos A = sin A + cos A
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Step-by-step explanation:
Answer:
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
Step-by-step explanation:
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