tan x+cosx=2 solve the equation
Answers
Answered by
1
Step-by-step explanation:
x
=
sin
−
1
(
−
1
+
√
17
4
)
Explanation:
Since
tan
x
=
sin
x
cos
x
, you can substitute:
tan
x
cos
x
=
sin
x
cos
x
cos
x
=
sin
x
cos
2
x
Since
cos
2
x
=
1
−
sin
2
x
, the given equation becomes:
sin
x
1
−
sin
2
x
=
2
It is equivalent to:
sin
x
=
2
(
1
−
sin
2
x
)
and
cos
x
≠
0
2
sin
2
x
+
sin
x
−
2
=
0
and
x
≠
π
2
+
k
π
sin
x
=
−
1
±
√
1
+
16
4
Case when
sin
x
<
−
1
can be dropped:
the solution
sin
x
=
−
1
−
√
17
4
<
−
1
the range of sin x is [-1;1] therefore
The solution is
sin
x
=
−
1
+
√
17
4
x
=
sin
−
1
(
−
1
+
√
17
4
)
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