What is the value of cosec A sec A cot A - sec A cosec A tan A?
What is the value of cosec A sec A cot A - sec A cosec A tan A?
1). \(2cotA + \;ta{n^2}A\)
2). \(co{t^2}A - \;ta{n^2}A\)
3). \(co{t^2}A - \;2tanA\)
4). \(co{t^2}A + \;ta{n^2}A\)
1 answers
Consider,
cosec A sec A cot A - sec A cosec A tan A
$(\Rightarrow \frac{1}{{\sin A}}\;\frac{1}{{cosA}}\;\frac{{cosA}}{{sinA}} - \frac{1}{{cosA}}\frac{1}{{sinA}}\frac{{sinA}}{{cosA}}\;\left[ {\because cosecA = \;\frac{1}{{sinA}};secA = \frac{1}{{cosA}};tanA = \frac{{sinA}}{{cosA}};cotA = \frac{{cosA}}{{sinA}}} \right])$
$(\begin{array}{l} \Rightarrow \frac{1}{{si{n^2}A}} - \;\frac{1}{{co{s^2}A}}\\ \Rightarrow cose{c^2}A - \;se{c^2}A \end{array})$
$( \Rightarrow 1 + \;co{t^2}A - 1 - ta{n^2}A\;\left[ {\because1 + ta{n^2}A = \;se{c^2}A;1 + co{t^2}A = \;cose{c^2}A} \right])$
$(\Rightarrow co{t^2}A - \;ta{n^2}A)$
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