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Cristina
Mathematics
27 July, 20:56
Find cos (a), if cos (a) ^4 - sin (a) ^4 = 1/8
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Miranda Cannon
27 July, 21:23
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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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