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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Allied Angles
Solve sin2π...
Question
Solve
sin
2
π
4
+
sin
2
3
π
4
+
sin
2
5
π
4
+
sin
2
7
π
4
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Solution
We know, that
sin
3
π
4
=
sin
(
π
2
+
π
4
)
=
cos
π
4
sin
5
π
4
=
sin
(
3
π
2
−
π
4
)
=
−
cos
π
4
sin
7
π
4
=
sin
(
2
π
−
π
4
)
=
−
sin
π
4
Now,
sin
2
π
4
+
sin
2
3
π
4
+
sin
2
5
π
4
+
sin
2
7
π
4
=
sin
2
π
4
+
cos
2
π
4
+
cos
2
π
4
+
sin
2
π
4
=
1
+
1
=
2
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