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# Example of finding the value of cosine double alfa

Question:

Given: tan a = 1/2, find the value of cos 2a.

Solution:

- from definition: tan a = sin a/cos a
- since tan a = 1/2 (given), so, sin a/cos a = 1/2
- use the cross multiplication
- so, cos a = 2 sin a
- square both side of the equation
- cos
^{2}a = 4 sin^{2}a, name this as equation1 - using the formula, sin
^{2}a + cos^{2}a = 1, name this as equation2 - substitute equation1 into equation2 to remove cos a
- sin
^{2}a + 4 sin^{2}a = 1 - 5 sin
^{2}a = 1 - sin
^{2}a = 1/5 - using the double angle formula,
- cos2a = 1 - 2 sin
^{2}a - so, cos2a = 1 - 2 sin
^{2}a = 1 - 2 × 1/5 = 5/5 - 2/5 = 3/5

Therefore, cos2a = 3/5. Looking for more detail? Please watch the video.