Simplify \sec A (1 - \sin A) (\sec A + \tan A)

Step 1: Take the given equation and simplify
GIVEN: \sec A(1 - \sin A)(\sec A + \tan A)
Multiply the \sec A inside the bracket
\left(\sec A-\sec A\sin A)(\sec A+\tan A\right)
Step 2: For simplification write the equivalent trigonometric ratios
EXAMPLE: \left(\sec A-\frac{1}{\cos A}\sin A)(\sec A+\tan A\right)
= \left(\sec A-\tan A)(\sec A+\tan A\right) (Since, \tan A = \frac{\sin A}{\cos A}
Multiply
= \left(\sec^2A+\sec A\tan A-\tan A\sec A-\tan^2A\right)
= \left(\sec^2A-\tan^2A\right)
= 1 (Since, \sec^2 A - \tan^2 A = 1 )