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Byju's Answer
Standard XII
Mathematics
Properties Derived from Trigonometric Identities
Prove the fol...
Question
Prove the following identities (1-16)
1
-
sin
2
x
1
+
cot
x
-
cos
2
x
1
+
tan
x
=
sin
x
cos
x
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Solution
1
-
sin
2
x
1
+
cot
x
-
cos
2
x
1
+
tan
x
=
sin
x
cos
x
LHS
=
1
-
sin
3
x
sin
x
+
cos
x
-
cos
3
x
sin
x
+
cos
x
=
sin
x
+
cos
x
-
sin
3
x
+
cos
3
x
sin
x
+
cos
x
=
sin
x
+
cos
x
1
-
sin
2
x
-
cos
2
x
+
sin
x
cos
x
sin
x
+
cos
x
=
1
-
sin
2
x
-
cos
2
x
+
sin
x
cos
x
=
1
-
1
+
sin
x
cos
x
=
sin
x
cos
x
= RHS
Hence proved.
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