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