Find cos (a), if cos (a) ^4 - sin (a) ^4 = 1/8

3/4, - 3/4

Step-by-step explanation:

Using the difference of squares we can change things around.

cos (a) ^4 - sin (a) ^4

(cos^2 (a) + sin^2 (a)) ((cos^2 (a) - sin^2 (a)) then sin^2 + cos^2 = 1

cos^2 (a) - sin^2 (a) Using the same identity sin^2 = 1 - cos^2

cos^2 (a) - (1 - cos^2 (a))

cos^2 (a) - 1 + cos^2 (a)

2*cos^2 (a) - 1

So let's use this.

2*cos^2 (a) - 1 = 1/8

2*cos^2 (a) = 9/8

cos^2 (a) = 9/16

cos (a) = + / - 3/4

so 3/4 can be positive or negative