Verify the identity. COs X = sec x + tan x 1 - sin x Working with the left-hand side, multiply the numerator and denominator by the conjugate of the denominator, and find the product in the denominator. (Simplify at each step.) cos x(1 + sin x) COS X 1 - sin x = (1 - sin x) cos x(1 + sin x) = 1 . Then, use the Pythagorean Identity for cos x, and simplify by dividing out the common factors. (Simplify at each step.) cos x(1 + sin x) LHS = 1 + sin x) Finally, rewrite the fraction as two fractions, and then use a Reciprocal Identity and a Ratio Identity to simplify. (Simplify at each step.) 1 sin X LHS =