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Byju's Answer
Standard XII
Mathematics
General Solution of Trigonometric Equation
Prove that ...
Question
Prove that
c
o
s
A
c
o
s
e
c
A
−
s
i
n
A
s
e
c
A
c
o
s
A
+
s
i
n
A
=
c
o
s
e
c
A
−
s
e
c
A
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Solution
LHS
=
c
o
s
A
c
o
s
e
c
A
−
s
i
n
A
s
e
c
A
c
o
s
A
+
s
i
n
A
=
cos
2
A
−
sin
2
A
sin
A
cos
A
(
cos
A
+
sin
A
)
=
(
cos
A
−
sin
A
)
(
cos
A
+
sin
A
)
sin
A
cos
A
(
cos
A
+
sin
A
)
=
cos
A
−
sin
A
sin
A
cos
A
=
1
s
i
n
A
−
1
c
o
s
A
=
c
o
s
e
c
A
−
sec
A
=
R
H
S
Hence proved
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Similar questions
Q.
Prove the following trigonometric identities.
(i)
cos
A
cosec
A
-
sin
A
sec
A
cos
A
+
sin
A
=
cosec
A
-
sec
A
(ii)
sin
A
sec
A
+
tan
A
-
1
+
cos
A
cosec
A
+
cot
A
-
1
=
1