Question
Asked Nov 21, 2019
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Solve the equation for exact solutions over the interval [0, 2π).

sec2x - 2 = tan2x

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Expert Answer

Step 1

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sec2x-2 tan 2x = 0 sin 2x -0 cos2x 1 -2 cos2x 1-sin 2x 2 cos2x = 0 1-sin 2x 2cos2x

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Step 2

Now, square on both sides.

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1 sin 2x 2cos 2x (1-sin 2x4 cos2 2x (1-sin 2x-4(1-sin 2x) 0 [ sin x +cos'x-1] 1-2 sin 2xsin2 2x -4+ 4sin2 2x = 0 5 sin 2x-2 sin 2x -3 0

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Step 3

...
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5u? - 5u + 3и —3%3D 0 Su(и -1) +3(и-1) -о (5и+ 3)(и-1) - о 3 и%3D- -,1 5

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Tagged in

Math

Trigonometry

Inverse Trigonometric Ratios