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Byju's Answer
Standard XII
Mathematics
Properties Derived from Trigonometric Identities
If x+tan x=k,...
Question
If sec x + tan x = k, cos x =
(a)
k
2
+
1
2
k
(b)
2
k
k
2
+
1
(c)
k
k
2
+
1
(d)
k
k
2
-
1
Open in App
Solution
(b)
2
k
k
2
+
1
We
have
:
sec
x
+
tan
x
=
k
1
⇒
1
sec
x
+
tan
x
=
1
k
⇒
sec
2
x
-
tan
2
x
sec
x
+
tan
x
=
1
k
⇒
sec
x
+
tan
x
sec
x
-
tan
x
sec
x
+
tan
x
=
1
k
∴
s
e
c
x
-
tan
x
=
1
k
2
Adding
1
and
2
:
2
sec
x
=
k
+
1
k
⇒
2
sec
x
=
k
2
+
1
k
⇒
sec
x
=
k
2
+
1
2
k
⇒
1
cos
x
=
k
2
+
1
2
k
⇒
cos
x
=
2
k
k
2
+
1
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11
Similar questions
Q.
If sec θ + tan θ = k, cos θ =
(a)
k
2
+
1
2
k
(b)
2
k
k
2
+
1
(c)
k
k
2
+
1
(d)
k
k
2
-
1
Q.
Consider matrix
A
=
[
k
2
k
k
2
−
k
k
2
]
and vector x=
[
x
1
x
2
]
. The number of distinct real values of k for which the equation Ax=0 has infinitely many solutions is ______ .
Q.
If
sec
x
+
tan
x
=
k
, then show that
sin
x
=
k
2
−
1
k
2
+
1
.
Q.
If sec
x
+
tan
x
=
k
,then show that
sin
x
=
k
2
−
1
k
2
+
1
?
Q.
If
s
e
c
θ
+
t
a
n
θ
=
k
,
c
o
s
θ
=
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