A) \[\frac{-2}{3}\]
B) \[\frac{-3}{4}\]
C) \[\frac{2}{3}\]
D) \[\frac{3}{4}\]
Correct Answer: D
Solution :
| [d] We have, \[\tan \theta =\frac{1}{\sqrt{7}}\,\,\,\,\Rightarrow \,\,\,\,\cot \theta =\sqrt{7}\] |
| We know, |
| \[{{\sec }^{2}}\theta =(1+{{\tan }^{2}}\theta )=\left( 1+{{\left( \frac{1}{\sqrt{7}} \right)}^{2}} \right)=\left( 1+\frac{1}{7} \right)=\frac{8}{7}\] |
| and \[\cos e{{c}^{2}}\theta =(1+{{\cot }^{2}}\theta )=(1+{{(\sqrt{7})}^{2}})=(1+7)=8\] |
| \[\therefore \,\,\,\,\,\frac{\cos e{{c}^{2}}\theta -{{\sec }^{2}}\theta }{\cos e{{c}^{2}}\theta +{{\sec }^{2}}\theta }=\frac{\left( 8-\frac{8}{7} \right)}{\left( 8+\frac{8}{7} \right)}=\frac{48}{64}=\frac{3}{4}\] |
You need to login to perform this action.
You will be redirected in
3 sec
