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

Mathematics

1 answer:

Alex17521 [72]3 years ago

5 0

Answer:

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

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