if sec A - tanA= 4 , prove that cosA = 8/17
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Answers
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Step-by-step explanation:
Multiply both sides with
cos
x
we get
tan
A
+
sec
A
=
4
⇒
1
+
sin
A
=
4
cos
A
Square both sides in the last one
1
+
2
sin
A
+
sin
2
A
=
16
cos
2
A
⇒
1
+
2
√
1
−
cos
2
A
=
16
cos
2
A
−
(
1
−
cos
2
A
)
⇒
2
√
1
−
cos
2
A
=
17
cos
2
A
−
2
Solving
2
√
1
−
cos
2
A
=
17
cos
2
A
−
2
with respect to
cos
A
we get
cos
A
=
±
8
17
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