Question

$\sf \: Simplify \: \sec A \: (1 - \sin A ) \: (sin A + tan A).$
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Answer 1

$\\ tan (a) \: +sec (a) \: tan (a) \: — sin \: (a) \: tan \: (a) \: \\ \\ \\ \\ - tan² (a)$

Answer 2

Answer:

${ \large{ \underline{ \pmb{ \sf{ \red{Correct \: Question : }}}}}}$

${\sf{SecA(1-SinA)(SecA+TanA)}}$

${ \large{ \underline{ \pmb{ \sf{ \red{Solution:}}}}}}$

${ \longmapsto { \sf{ \frac{1}{CosA} (1-SinA)\bigg\{ \frac{1}{CosA}+ \frac{SinA}{CosA} \bigg\} }}}$

${ \longmapsto{ \sf{ \frac{1-SinA}{CosA} \bigg \{ \frac{1+SinA}{CosA}\bigg\} }}}$

${ \longmapsto{ \sf{ \frac{(1+SinA)(1-SinA)}{Cos²A} }}}$

${ \longmapsto{ \sf{ \frac{1 - {Sin}^{2} A}{ {Cos}^{2} A} }}}$

${ \longmapsto{ \sf{ \frac{ {Cos}^{2} A}{ {Cos}^{2}A } }}}$

${ \longmapsto{ \sf{1}}}$

${ \therefore{ \underline{ \pmb{{\sf{SecA(1-SinA)(SecA+TanA) = 1}}}}}}$