Question

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Answer 1

Step-by-step explanation:

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Answer 2

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$\tt{ \large{ \underline{ \underline{ \orange{Answer}}}}}: - \\ \bf{Prove \: that,} \\ \bf{ \frac{1}{sinA + cosA} + \frac{1}{sinA - cosA} = \frac{2sinA}{1 - 2 {cos}^{2} A}} \\ \\ \tt{ \large{ \underline{ \underline{ \blue{Solution}}}}}: - \\ \sf{ \underline{L.H.S.}}\\ \\ \\ \bf{Formulas \: used}: \\ \boxed{ \bf{ {sin}^{2}A = 1 - {cos}^{2} A }} \\ \boxed{ \bf{ {a}^{2} - {b}^{2} = (a + b)(a - b)}} \\ \\ \\ \longrightarrow \bf \frac{1}{sinA + cosA} + \frac{1}{sinA - cosA} \\ \longrightarrow \bf \frac{sinA - \cancel{cosA} + sinA + \cancel{ cosA}}{(sinA + cosA)(sinA - cosA)} \\ \longrightarrow \bf \frac{2sinA}{ {sin}^{2} A - {cos}^{2}A } \\ \longrightarrow \bf \frac{2sinA}{1 - {cos}^{2}A - {cos}^{2}A } \\ \longrightarrow \bf \frac{2sinA}{1 - 2 {cos}^{2} A} = \sf{R.H.S.} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \purple{ \mathbb{(PROVED)}}$