Question
$$\begin{aligned}&\text { If } \tan B=\frac{n \sin A \cos A}{1-n \sin ^{2} A}, \text { show that }\\&\tan (A-B)=(1-n) \tan A\end{aligned}$$
Step 1
Substituting the given value of $\tan B$ in this equation, we get \[\tan(A-B) = \frac{\tan A - \frac{n \sin A \cos A}{1-n \sin ^{2} A}}{1 + \tan A \cdot \frac{n \sin A \cos A}{1-n \sin ^{2} A}}.\] Show more…
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