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Byju's Answer
Standard X
Mathematics
Trigonometric Identities
Which of the ...
Question
Which of the following is a trigonometric identity?
A
1
+
s
e
c
2
θ
=
t
a
n
2
θ
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B
1
+
c
o
s
e
c
2
θ
=
c
o
t
2
θ
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C
s
i
n
2
θ
=
1
−
c
o
s
2
θ
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D
s
i
n
2
θ
−
c
o
s
2
θ
=
1
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Solution
The correct option is
C
s
i
n
2
θ
=
1
−
c
o
s
2
θ
We know that,
s
i
n
2
θ
+
c
o
s
2
θ
=
1
t
a
n
2
θ
+
1
=
s
e
c
2
θ
c
o
t
2
θ
+
1
=
c
o
s
e
c
2
θ
∴
s
i
n
2
θ
=
1
−
c
o
s
2
θ
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0
Similar questions
Q.
Prove that
(
1
s
e
c
2
θ
−
c
o
s
2
θ
+
1
c
o
s
e
c
2
θ
−
s
i
n
2
θ
)
s
i
n
2
θ
cos
2
θ
=
1
−
sin
2
θ
c
o
s
2
θ
2
+
s
i
n
2
θ
c
o
s
2
θ
Q.
sec
2
θ
−
sin
2
θ
−
2
sin
4
θ
2
cos
4
θ
−
cos
2
θ
=
1
.
Q.
Prove the following identity
tan
2
θ
tan
2
θ
−
1
+
c
o
s
e
c
2
θ
sec
2
θ
−
c
o
s
e
c
2
θ
=
1
sin
2
θ
−
cos
2
θ
Q.
Square relations among various trigonometrical ratios
sin
2
θ
+
cos
2
θ
=
1
sec
2
θ
−
tan
2
=
1
cos
e
c
2
θ
−
cot
2
θ
=
1
These are also called Pythagorean identities.
Q.
Choose the correct answer from the alternatives given.
If
0
<
θ
<
90
∘
then what is the minimum value of
s
i
n
2
θ
+
c
o
s
2
θ
+
t
a
n
2
θ
+
c
o
t
2
θ
+
s
e
c
2
θ
+
+
c
o
s
e
c
2
θ
?
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