1). $2cotA + \;ta{n^2}A$2). $co{t^2}A - \;ta{n^2}A$3). \(co{t^2}A

1.	1). \(2cotA + \;ta{n^2}A\)2). \(co{t^2}A - \;ta{n^2}A\)3). \(co{t^2}A - \;2tanA\)4). \(co{t^2}A + \;ta{n^2}A\)
Answer» CONSIDER, cosec A sec A COT A - sec A cosec A tan A $(\RIGHTARROW \frac{1}{{\sin A}}\;\frac{1}{{cosA}}\;\frac{{cosA}}{{sinA}} - \frac{1}{{cosA}}\frac{1}{{sinA}}\frac{{sinA}}{{cosA}}\;\left[ {\because cosecA = \;\frac{1}{{sinA}};SECA = \frac{1}{{cosA}};tanA = \frac{{sinA}}{{cosA}};cotA = \frac{{cosA}}{{sinA}}} \right])$ $(\begin{array}{l} \Rightarrow \frac{1}{{si{n^2}A}} - \;\frac{1}{{co{s^2}A}}\\ \Rightarrow cose{c^2}A - \;se{c^2}A\end{array})$ $( \Rightarrow 1 + \;co{t^2}A - 1 - ta{n^2}A\;\left[ {\because1 + ta{n^2}A = \;se{c^2}A;1 + co{t^2}A = \;cose{c^2}A} \right])$ $(\Rightarrow co{t^2}A - \;ta{n^2}A)$

1). $2cotA + \;ta{n^2}A$2). $co{t^2}A - \;ta{n^2}A$3). $co{t^2}A - \;2tanA$4). $co{t^2}A + \;ta{n^2}A$

Answer»

cosec A sec A COT A - sec A cosec A tan A

$(\RIGHTARROW \frac{1}{{\sin A}}\;\frac{1}{{cosA}}\;\frac{{cosA}}{{sinA}} - \frac{1}{{cosA}}\frac{1}{{sinA}}\frac{{sinA}}{{cosA}}\;\left[ {\because cosecA = \;\frac{1}{{sinA}};SECA = \frac{1}{{cosA}};tanA = \frac{{sinA}}{{cosA}};cotA = \frac{{cosA}}{{sinA}}} \right])$

$(\begin{array}{l} \Rightarrow \frac{1}{{si{n^2}A}} - \;\frac{1}{{co{s^2}A}}\\ \Rightarrow cose{c^2}A - \;se{c^2}A\end{array})$

$( \Rightarrow 1 + \;co{t^2}A - 1 - ta{n^2}A\;\left[ {\because1 + ta{n^2}A = \;se{c^2}A;1 + co{t^2}A = \;cose{c^2}A} \right])$

$(\Rightarrow co{t^2}A - \;ta{n^2}A)$

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