
Lois C. answered 04/01/20
Knowledgeable, experienced tutor specializing in secondary mathematics
To prove this, we need only work with the left side of the equation. We begin by replacing sin 2x in the numerator with its equivalent expression 2 sin x cos x ( via the double-angle identity for sine). We then replace the denominator with cos2 x ( via the first of the three Pythagorean Identities). We then cancel out the common factors of cos x in numerator and denominator, which leaves us with 2 sinx/cos x, and this is equivalent to 2 tan x, which now matches the right side of the equation.