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Byju's Answer
Standard X
Mathematics
Trigonometric Identities
Prove that : ...
Question
Prove that :
(
1
−
sin
θ
+
cos
θ
)
2
=
2
(
1
+
cos
θ
)
(
1
−
sin
θ
)
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Solution
L
H
S
=
(
1
−
s
i
n
θ
+
c
o
s
θ
)
2
L
H
S
=
1
+
s
i
n
2
θ
+
c
o
s
2
θ
−
2
s
i
n
θ
+
2
c
o
s
θ
−
2
s
i
n
θ
c
o
s
θ
L
H
S
=
2
−
2
s
i
n
θ
+
2
c
o
s
θ
−
2
s
i
n
θ
c
o
s
θ
L
H
S
=
2
(
1
−
s
i
n
θ
)
+
2
c
o
s
θ
(
1
−
s
i
n
θ
)
L
H
S
=
2
(
1
−
s
i
n
θ
)
(
1
+
c
o
s
θ
)
=
R
H
S
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Similar questions
Q.
Prove the following trigonometric identities.
(i)
1
+
sin
θ
-
cos
θ
1
+
sin
θ
+
cos
θ
2
=
1
-
cos
θ
1
+
cos
θ
(ii)
1
+
sec
θ
-
tan
θ
1
+
sec
θ
+
tan
θ
=
1
-
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cos
θ