favicon learning mathematics at the website of mathtestpreparation.com
back to Trigonometry video lessons

How to find cos2a from tan a?

Question:

If tan a = 5, what is the value of cos 2a?

Solution:

by definition: tan a = sin a/cos a
given: tan a = 5, then sin a/cos a = 5
so, sin a = 5 cos a
square both sides of the equation
sin2a = (5 cos a)2
= 25 cos2a
so, sin2a = 25 cos2a, name this as equation1
using sin2a + cos2a = 1, name this as equation2
substitute equation1 into equation2
25 cos2a + cos2a = 1
26 cos2a = 1
cos2a = 1/26
using the double angle formula
cos2a = 2 cos2a - 1
= 2 × (1/26) - 1
= 2/26 - 1
=1/13 - 1
=1/13 - 13/13
= - 12/13

Therefore, the value of cos 2a is -12/13. Watch the video for more details.

© www.mathtestpreparation.com