A) \[\frac{25}{7}\]
B) \[\frac{7}{25}\]
C) \[\frac{6}{25}\]
D) \[\frac{11}{25}\]
Correct Answer: B
Solution :
\[\cot \theta =\frac{4}{3}\Rightarrow {{\cot }^{2}}\theta =\frac{16}{9}\] \[1+{{\cot }^{2}}\theta =1+\frac{16}{9}\,\,\,\,\Rightarrow \,\,\,{{\operatorname{cosec}}^{2}}\theta =\frac{25}{9}\] \[\therefore \,\,\,\,\,\,\text{cosec }\theta =\frac{5}{3}\,\,\,\Rightarrow \,\,\,\sin =\frac{3}{5}\] \[\therefore \,\,\,\,\,\,\text{co}{{\text{s}}^{2}}\theta =1-2\,{{\sin }^{2}}\theta \] \[=\,\,\,\,\,1-2\times \frac{9}{25}=\frac{1}{1}-\frac{18}{25}\] \[=\,\,\,\,\,\,\,\frac{25-18}{25}=\underline{\frac{\mathbf{7}}{\mathbf{25}}}\]
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