If x is an acute angle, and cos x =4/5, then cos (2 x) is equal to?

1 Answer
Apr 28, 2018

#cos 2x = 7/25#

Explanation:

Use trig identity:
#cos 2x = 2cos^2 x - 1#
In this case:
#cos 2x = (2)(16/25) - 1 = 32/25 - 25/25 = 7/25#
To find the sign of cos 2x, use calculator to approximately get the value of x and 2x.
#cos x = 4/5# --> #x = 36^@87# --> #2x = 73^@74#.
Since 2x is in Quadrant 1, then, cos 2x is positive.
#cos 2x = 7/25#