Question

prove ( sec A + tan A ) ( 1 - sin A ) = cos A
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Answer 1

it will definitely help you

Answer 2

Answer:

$\large\bf\underline\red{Question ➡} \\ \\\bf prove \: that : - \\ \bf \: (secA \: + tanA)(1 - sinA) = cosA \\ \\ \large\bf\underline\blue{some \: basic \: information➡} \\ \\ \bf\bigstar \: secA \: = \frac{1}{cosA} \\ \\ \bf\bigstar \:tanA = \frac{sinA}{cosA} \\ \\ \bf\bigstar \: 1 - {sinA}^{2} = {cosA}^{2} \\ \\ \large\bf\underline\blue{solution➡} \: \\ \\ \sf \: (secA \: + tanA)(1 - sinA) = cosA \\ \\\bf \underline{LHS} \\ \\➡\sf \: ( \frac{1}{cosA} + \frac{sinA }{cosA} )(1 - sinA) \\ \\ ➡\sf \: ( \frac{1 +sinA }{cosA} )(1 - sinA) \\ \\ ➡\sf \: \frac{1 - {sinA}^{2} }{cosA} \\ \\ \sf \underline{(using \: 1 - {sinA}^{2} = {cosA}^{2} ) } \\ \\ ➡\sf \: \frac{ {cosA}^{2} }{cosA} \\ ➡\sf \: \frac{ { \cancel{¹cosA}}^{2} }{ \cancel{cosA} } \\ \\➡\sf \: cosA \\ \\➡\sf \: RHS \\ \\ \bf \underline{therefore : - } \\ \\\large{\boxed{\mathtt\red{\fcolorbox{magenta}{aqua}{LHS=RHS}}}}$