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Byju's Answer
Standard IX
Mathematics
Calculating Heights and Distances
Prove the fol...
Question
Prove the following :
(ix)
1
cos
e
c
A
-
c
o
t
A
-
1
sin
A
=
1
S
i
n
A
-
1
cos
e
c
A
+
c
o
t
A
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Solution
We
can
write
1
cos
e
c
A
-
c
o
t
A
-
1
sin
A
=
1
sin
A
-
1
cos
e
c
A
+
c
o
t
A
as
1
cos
e
c
A
-
c
o
t
A
+
1
cos
e
c
A
+
c
o
t
A
=
1
sin
A
+
1
sin
A
=
2
sin
A
.
.
.
(
i
)
So
,
we
can
prove
the
above
identity
in
place
of
1
cos
e
c
A
-
c
o
t
A
-
1
sin
A
=
1
sin
A
-
1
cos
e
c
A
+
c
o
t
A
.
Taking
LHS
of
(
i
)
,
we
have
:
1
cos
e
c
A
-
c
o
t
A
+
1
cos
e
c
A
+
c
o
t
A
=
cos
e
c
A
+
c
o
t
A
+
cos
e
c
A
-
c
o
t
A
cos
e
c
2
A
-
c
o
t
2
A
=
2
cos
e
c
A
=
2
sin
A
=
RHS
of
(
i
)
Hence, proved.
Suggest Corrections
2
Similar questions
Q.
Prove
that
cot
A
−
cos
A
cot
A
+
cos
A
=
cos
e
c
A
−
1
cos
e
c
A
+
1
Q.
Prove the following trigonometric identities.
cot
A
-
cos
A
cot
A
+
cos
A
=
cosec
A
-
1
cosec
A
+
1
