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Byju's Answer
Standard XII
Mathematics
Chain Rule of Differentiation
Prove that ...
Question
Prove that
(
s
e
c
θ
+
c
o
s
θ
)
(
s
e
c
θ
−
c
o
s
θ
)
=
t
a
n
2
θ
+
s
i
n
2
θ
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Solution
L
.
H
.
S
=
(
sec
θ
+
c
o
s
θ
)
(
sec
θ
−
cos
θ
)
=
sec
2
θ
−
cos
2
θ
=
1
+
tan
2
θ
−
cos
2
θ
[
∵
1
+
tan
2
θ
=
sec
2
θ
]
=
tan
2
θ
+
1
−
cos
2
θ
=
tan
2
θ
+
sin
2
θ
[
∵
sin
2
θ
+
cos
2
θ
=
1
]
=
R
.
H
.
S
∴
(
sec
θ
+
c
o
s
θ
)
(
sec
θ
−
cos
θ
)
=
tan
2
θ
+
sin
2
θ
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Q.
Prove the following trigonometric identities.
(secθ + cosθ) (secθ − cosθ) = tan
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