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What is the simplified value of \(\frac{{cotA + tanB}}{{cotB + tanA}}\) ?1). tan B cot A2). tan A cot B3). tan A tan B4). cot A cot B

Answer»

$(\begin{ARRAY}{l}\frac{{cotA + TANB}}{{COTB + tanA}}\\ \Rightarrow \frac{{\frac{{cosA}}{{sinA}} + \frac{{SINB}}{{cosB}}}}{{\frac{{cosB}}{{sinB}} + \frac{{sinA}}{{cosA}}}}\\ \Rightarrow \frac{{cosA\;cosB + sinA\;sinB}}{{cosA\;cosB + sinA\;sinB}} \TIMES \frac{{sinB\;cosA}}{{sinA\;cosB}}\end{array})$

⇒ tanB cotA



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