Solve the equation sec^2(A) = 3 - tan(A), for 0<= A <= 360 (degrees)
Using simple trig identities, we know tan^2(A) + 1 = sec^2(A).Substituting for sec^2(A) into our equation, we get: tan^2(A) + 1 = 3 - tan(A).Moving this over to one side, we get the quadratic in terms of tan(A), tan^2(A) +tan(A) - 2 = 0.Now we can solve since the equation is equal to 0, so we can factorise in terms of tan(A).(Tan(A) - 1)(Tan(A) + 2) = 0Since both brackets must be equal to zero, tan(A) = 1, and tan(A) = -2Now if you perform arctan on these two values, you get A = 45, 225 or 116.6, 296.6
LF
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