prove that :cos^4(pi/8)+cos^4(3 pi/8)+sin^4(5 pi/8)+sin^4(7 pi/8)=3/2
Answers
Answered by
0
テリマキシュートセールジェイクアプニガンドマラオ
Answered by
1
Answer:
Let
π
8
=
x
then
8
x
=
π
and
4
x
=
π
2
L
H
S
=
cos
2
(
π
8
)
+
cos
2
(
3
π
8
)
+
cos
2
(
5
π
8
)
+
cos
2
(
7
π
8
)
=
cos
2
x
+
cos
2
(
3
x
)
+
cos
2
(
5
x
)
+
cos
2
(
7
x
)
=
cos
2
x
+
cos
2
(
3
x
)
+
cos
2
(
4
x
+
x
)
+
cos
2
(
4
x
+
3
x
)
=cos2x+cos2(3x)+cos2(π2+x)+cos2(π2+3x)=cos2x+cos2(3x)+sin2(x)+sin2(3x)=1+1=2=RHS
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