What is the expression that remains when we simplify $(s e c A + t a n A) (1 - s i n A)$ ?

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Solution

$(s e c A + t a n A) (1 - s i n A)$

= $(\frac{1}{c o s A} + \frac{s i n A}{c o s A}) (1 - s i n A)$
= $\frac{1 + s i n A}{c o s A} \times (1 - s i n A)$
= $\frac{1 - s i n^{2} A}{c o s A}$
= $\frac{c o s^{2} A}{c o s A} = c o s A$

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