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If tanA = 15/8 and tanB = 7/24, then tan(A-B)?
- A304/297
- B304/425
- C416/87
- D87/416
Answer not set
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CCommunity
We know that,
$(\begin{array}{l}
{\rm{tan}}\left( {{\rm{x}} - {\rm{y}}} \right){\rm{\;}} = {\rm{\;}}\frac{{{\rm{tanx}} - {\rm{tany}}}}{{1{\rm{\;}} + {\rm{\;tanxtany}}}}\\
\Rightarrow {\rm{\;}}tan\left( {A - B} \right)\; = \;\frac{{tanA - tanB}}{{1\; + \;tanAtanB}}\; = \;\frac{{\frac{{15}}{8} - \frac{7}{{24}}}}{{1\; + \;\frac{{15}}{8} \times \frac{7}{{24}}}}\; = \;\frac{{304}}{{297}}
\end{array})$
∴ tan(A – B) = 304/297
$(\begin{array}{l}
{\rm{tan}}\left( {{\rm{x}} - {\rm{y}}} \right){\rm{\;}} = {\rm{\;}}\frac{{{\rm{tanx}} - {\rm{tany}}}}{{1{\rm{\;}} + {\rm{\;tanxtany}}}}\\
\Rightarrow {\rm{\;}}tan\left( {A - B} \right)\; = \;\frac{{tanA - tanB}}{{1\; + \;tanAtanB}}\; = \;\frac{{\frac{{15}}{8} - \frac{7}{{24}}}}{{1\; + \;\frac{{15}}{8} \times \frac{7}{{24}}}}\; = \;\frac{{304}}{{297}}
\end{array})$
∴ tan(A – B) = 304/297