Question

8secx - 3tan^2(x) =7 0 < x < 360 Find the 2 angles that satisfy this equation

Answer 1

The two angles that satisfy this equation are 60 degrees and 300 degrees

Trigonometric identities

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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