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Byju's Answer
Standard XII
Mathematics
Properties Derived from Trigonometric Identities
The maximum v...
Question
The maximum value of
sin
θ
+
cos
θ
is
A
1
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B
2
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C
3
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D
√
2
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Solution
The correct option is
C
√
2
Formula used:
sin
(
α
+
β
)
=
sin
α
cos
β
+
cos
α
sin
β
sin
θ
+
cos
θ
=
√
2
(
1
√
2
sin
θ
+
1
√
2
cos
θ
)
=
√
2
(
cos
45
∘
sin
θ
+
sin
45
∘
cos
θ
)
=
√
2
sin
(
45
∘
+
θ
)
and maximum value of
sin
(
45
∘
+
θ
)
=
1
∴
maximum value of
sin
θ
+
cos
θ
=
√
2
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0
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