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Byju's Answer
Standard XII
Mathematics
Integration of Irrational Algebraic Fractions - 2
If sinθ=ab,...
Question
If
sin
θ
=
a
b
, show that
(
sec
θ
+
tan
θ
)
=
√
m
b
+
a
m
b
−
a
.
.Find
m
Open in App
Solution
sin
θ
=
a
b
=
P
H
(Refer to Image)
B
=
√
b
2
−
a
2
sec
θ
=
1
cos
θ
=
H
B
=
b
√
b
2
−
a
2
tan
θ
=
sin
θ
cos
θ
=
a
b
√
b
2
−
a
2
b
=
a
√
b
2
−
a
2
⇒
(
sec
θ
+
tan
θ
)
=
b
√
b
2
−
a
2
+
a
√
b
2
−
a
2
=
b
+
a
√
b
2
−
a
2
=
√
(
b
+
a
)
2
b
2
−
a
2
=
√
(
b
+
a
)
2
(
b
−
a
)
(
b
+
a
)
⇒
√
b
+
a
b
−
a
=
√
m
b
+
a
m
b
−
a
∴
m
=
1
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0
Similar questions
Q.
If
sec
θ
+
tan
θ
=
p
, show that
sec
θ
−
tan
θ
=
1
p
. Hence, find the values of
cos
θ
and
sin
θ
.
Q.
Show that
√
1
−
sin
θ
1
+
sin
θ
=
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θ
Q.
If
a
→
×
b
→
=
b
→
×
c
→
≠
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,
then show that
a
→
+
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→
=
m
b
→
,
where m is any scalar.
Q.
If (sec θ + tan θ ) = p then show that (sec θ – tan θ) =
1
p
.
Hence, show that cos θ =
2
p
p
2
+
1
and
sin
θ
=
p
2
-
1
p
2
+
1
.
Q.
If
s
i
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θ
=
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b
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in terms of
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Standard XII Mathematics
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