Question
Asked Oct 20, 2019
Prove the following identity
cos2 20
1
cos 20
cos4
=
4
2
4
We begin by using a Double-Angle Formula twice on the right side of the equation. We can then expand all products and add the fractions to simplify.
cos2 20
(2 cos2 0
2.
1)
cos 20
+
- 1
+
1
1
4
2
2
22.
- 1
0 - 4 cos2 e + 1
4 cos4
4
4
cos4 e
= COS
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Prove the following identity cos2 20 1 cos 20 cos4 = 4 2 4 We begin by using a Double-Angle Formula twice on the right side of the equation. We can then expand all products and add the fractions to simplify. cos2 20 (2 cos2 0 2. 1) cos 20 + - 1 + 1 1 4 2 2 22. - 1 0 - 4 cos2 e + 1 4 cos4 4 4 cos4 e = COS

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check_circleExpert Solution
Step 1

Given: -

1 cos 20 cos2 20
cos e
4
+
2
4
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1 cos 20 cos2 20 cos e 4 + 2 4

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Step 2

To find: -

To prove the given equation using double angle formula twice
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To prove the given equation using double angle formula twice

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Step 3

Calculation...

(2 cos' -1)
12cos0-
cos2 20
cos 20
1
4
2
4
4
2
4
2 cos - (2cos' 0-1)
=-
4
2
4
1 2cos20-1 2cos40-4cos2 0+1
4
2
4
1+4cos20-2+4 cos 0-4cos201
4
4cose
4
=cose
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(2 cos' -1) 12cos0- cos2 20 cos 20 1 4 2 4 4 2 4 2 cos - (2cos' 0-1) =- 4 2 4 1 2cos20-1 2cos40-4cos2 0+1 4 2 4 1+4cos20-2+4 cos 0-4cos201 4 4cose 4 =cose

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Math

Trigonometry