Find all solutions in the interval [0, 2π). sec2 x - 2 = tan2 x

1 answer:

maks197457 [2]2 years ago

3 0

The equation is equivalent to 1/cos(2x)-2=sin(2x)/cos(2x). Make the denominator cos(2x) for all terms, we get 1-2cos(2x)=sin(2x). Since cos^2(2x)+sin^2(2x)=1, let cos(2x)=a, substitute sin(2x) by +-\sqrt(1-a^2), and solve the equation with only one variable a. We get a=4/5 or 0, but cos(2x) cannot be 0, otherwise sec(2x) is undefined. 2x=36.9 degrees, so x=18.9 degrees approximately.

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Step-by-step explanation:

How to get the answer:

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Answer:

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Step-by-step explanation:

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