The two angles that satisfy this equation are 60 degrees and 300 degrees
<h3>Trigonometric identities</h3>
Trigonometry are expressed as a function of sine, cosine and tangent.
Given the trigonometry expression below;
8secx - 3tan^2(x) =7
Since tan^2x= sec^2x - 1
Substitute
8secx - 3(sec^2x-1) =7
Expand
8secx - 3sec^2x + 3 = 7
3sec^2x - 8secx +4 = 0
Let P = secx such that;
3P^2 - 8P - 4 = 0
Factorize
3P^2 - 6P -2 P + 4 = 0
3P(P - 2) - 2(P - 2) = 0
P - 2 = 0
P = 2
since secx = P, hence;
secx = 2
1/cosx = 2
cosx = 1/2
x = 60 degrees
Since cosine is positive in the fourth quadrant, hence;
x2 = 360 - 60
x2 = 300degrees
Hence the two angles that satisfy this equation are 60 degrees and 300 degrees
Learn more on trigonometry angles here: brainly.com/question/25716982
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