A) \[\sin \theta =\frac{{{a}^{2}}+{{b}^{2}}}{{{a}^{2}}-{{b}^{2}}},(a\ne b)\]
B) \[\sin \theta =\frac{4}{5}\]
C) \[\sin \theta =45\]
D) \[\cos \theta =\frac{7}{3}\]
Correct Answer: C
Solution :
(a) Suppose \[a=2,\] \[b=1\] \[\sin \theta =\frac{{{2}^{2}}+{{1}^{2}}}{{{2}^{2}}-1}=\frac{5}{3}>1,\] which is not possible. (b) \[\sec \theta =\frac{4}{5}<1,\] which is not possible (c) \[\tan \theta =45,\] which is possible (d) \[\cos \theta =\frac{7}{3}>1,\] which is not possible. Hence, option (c) is correct.
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