Question

(sec A + tan A) (1 − sin A) = ?
(a) sin A
(b) cos A
(c) sec A
(d) cosec A

Answer 1

(b) cos A

$\begin{array}{l}(\text{sec}A+\tan A)(1-\text{sin}A)\\ \text{=}(\frac{1}{\text{cos}A}+\frac{\text{sin}A}{\text{cos}A})(1-\text{sin}A)\\ =\left(\frac{1+\text{sin}A}{\text{cos}A}\right)(1-\text{sin}A)\\ =\left(\frac{1-{\text{sin}}^{2}A}{\text{cos}A}\right)\\ =\left(\frac{{\text{cos}}^{2}A}{\text{cos}A}\right)\\ =\text{cos}A\\ \end{array}$