Find a solution to sec^(2)(x)+2tan(x) = 0
This question is a quadratic equation in hiding. The first step to solving this would be to expand sec^(2)(x) into 1 + tan^(2)(x) as they are equivalent. This can be derived by dividing sin^(2)(x) + cos^(2)(x) = 1 by cos^(2)(x). This will give us the equation tan^(2)(x) + 2tan(x) +1 = 0. If tan(x) is set to equal z, we end up with the equation z^(2)+2z+1 = 0, which gives us the solution z = -1 when the quadratic formula is used. If we substitute tan(x) back in, we end up with tan(x) = -1, which gives us the solution x = -45 when our calculators are used.
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