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dalvyx [7]
3 years ago
14

Find all solutions in the interval [0,2pi) sec^2x + 2tanx = 3

Mathematics
1 answer:
Marysya12 [62]3 years ago
6 0
Tan^2x + 1 + tanx - 3 = 0 tan^2x + tanx - 2 = 0 (tanx + 2)(tanx - 1) = 0 tanx = -2 or tanx = 1 x = 2.034 radians or x = 5.176 radians or x = pi/4 radians or x = 5pi/4 radians
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How do you this question? Please explain.
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Recognize that all the triangles are right triangles, so are similar to each other. In these similar triangles, the ratio of the short side to the long side is the same for all.

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<em>Comment on this solution</em>

The altitude to the hypotenuse of a right triangle (CB in this case) divides the hypotenuse into lengths such that the altitude is their geometric mean. That is ...

... CB = √(AC·CT) . . . . as above

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