If $\sec{ heta = m}$ and $ an{ heta = n}$, then $\frac{1}{m}\left\lbrack (m + n) + \frac{1}{(m + n)} ight brack$ is

Question

If $\sec{	heta = m}$ and $	an{	heta = n}$, then $\frac{1}{m}\left\lbrack (m + n) + \frac{1}{(m + n)} ightbrack$ is

Dr. Abubacker · Accepted Answer

(a)
$\frac{1}{m}\left\lbrack (m + n) + \frac{1}{(m + n)} ightbrack$
$= \frac{1}{\sec	heta}\left\lbrack \sec{	heta + 	an{	heta + \frac{1}{\sec{	heta + 	an	heta}}}} ightbrack$
$= \frac{\lbrack\sec^{2}{	heta + 	an^{2}{	heta + 2\sec{	heta	an{	heta + 1}}}}brack}{\sec{	heta(\sec{	heta + 	an	heta})}}$
$= \frac{2\sec^{2}{	heta + 2\sec{	heta	an	heta}}}{\sec{	heta(\sec{	heta + 	an	heta})}}$
$= 2$

Q. If $\sec{\theta = m}$ and $\tan{\theta = n}$, then $\frac{1}{m}\left\lbrack (m + n) + \frac{1}{(m + n)} \right\rbrack$ is

Explanation

Reviewed by Dr. Abubacker

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