The correct option is A sec A (sec A + tan A) (1 sin A) = (1/cos A+ sin A/cos A) (1 sin A) = (1 + sin A/cos A) (1 sin A) = (1 sin^2A)/cos A ...

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Trigonometric Identities

A+tan A1-sin ...

Question

(sec A + tan A) (1 - sin A) =

sec A

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sin A

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cosec A

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cos A

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Solution

The correct option is
D

cos A

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

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Similar questions

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

(a) sin A (b) cos A (c) sec A (d) cosec A

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

[(sec A + tan A) (1 - sin A)] on simplification gives:

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