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Relation between Trigonometric Ratios

Question 4 ii...

Question

Question 4 (iii)
Choose the correct option. Justify your choice.
(iii) (sec A + tan A) (1 - sin A) =
(A) sec A
(B) sin A
(C) cosec A
(D) cos A

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Solution

(iii) (D) is correct.
$(s e c A + t a n A) (1 - s i n A)$
$= (\frac{1}{c o s A} + \frac{s i n A}{c o s A}) (1 - s i n A)$
$= (\frac{1 + s i n A}{c o s A}) (1 - s i n A)$
$= \frac{(1 - s i n^{2} A)}{c o s A}$
$= \frac{c o s^{2} A}{c o s A} = c o s A$

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