Question

(sec A + tan A)(1 - sin A)​

Answer 1

Answer:

$(secA + tanA)(1-sinA)\\\\ = (\frac{1}{cosA} + \frac{sinA}{cosA})(1-sinA)\\\\ = (\frac{1+sinA}{cosA})(1-sinA) \\\\=\frac{1-sin^{2}A }{cosA} \\\\=\frac{cos^{2}A }{cosA} \\\\=cosA$

Using the identity, $(1-sin^{2}A= cos^2A)$

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Answer 2

( 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 A) (1 - sin A ) /cos A

= ( 1 - sin 2 A) / cos A

= cos 2 A / cos A...................

$sin ^{2} + \cos^{2} = 1 \\ \cos^{2} = 1 - \sin^{2}$

=cos A