A) \[\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\]
B) \[\frac{{{b}^{2}}-{{a}^{2}}}{{{b}^{2}}+{{a}^{2}}}\]
C) \[\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}-{{b}^{2}}}\]
D) None of these
Correct Answer: A
Solution :
\[\frac{a\,\sin \,\theta -b\,\cos \,\theta }{a\,\sin \,\theta -b\,\cos \,\theta }=\frac{a\,\tan \,\theta -b}{a\,\tan \,\theta +b}\] \[=\frac{a\cdot \frac{a}{b}-b}{a\cdot \frac{a}{b}+b}=\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\] \[\left[ \tan \theta =\frac{a}{b}\,\,\text{(given)} \right]\]
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