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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Allied Angles
The value of$...
Question
The value of
sin
2
5
∘
+
sin
2
10
∘
+
sin
2
15
∘
+
sin
2
75
∘
+
sin
2
80
∘
+
sin
2
85
∘
+
sin
2
90
∘
is
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Solution
We know that
sin
2
85
∘
=
sin
2
(
90
∘
−
5
∘
)
=
cos
2
5
∘
∴
sin
2
5
∘
+
sin
2
85
∘
=
sin
2
5
∘
+
cos
2
5
∘
=
1
Similarly
sin
2
10
∘
+
sin
2
80
∘
=
sin
2
15
∘
+
sin
2
75
∘
=
1
Hence
sin
2
5
∘
+
sin
2
10
∘
+
sin
2
15
∘
+
sin
2
75
∘
+
sin
2
80
∘
+
sin
2
85
∘
+
sin
2
90
∘
=
1
+
1
+
1
+
1
=
4
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Trigonometric Ratios of Allied Angles
Standard XII Mathematics
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