A) \[2n\pi +\frac{\pi }{4}\]
B) \[2n\pi \pm \frac{\pi }{4}\]
C) \[2n\pi -\frac{\pi }{4}\]
D) None of these
Correct Answer: B
Solution :
\[2{{\cos }^{2}}\theta -(\sqrt{2}+1)\cos \theta -1+\frac{(\sqrt{2}+1)}{\sqrt{2}}=0\] \[\Rightarrow \] \[\cos \theta =\frac{(\sqrt{2}+1)\pm \sqrt{{{(\sqrt{2}+1)}^{2}}-\frac{8}{\sqrt{2}}}}{4}\] \[\Rightarrow \] \[\cos \theta =\cos \left( \frac{\pi }{4} \right)\] \[\Rightarrow \] \[\theta =2n\pi \pm \frac{\pi }{4}\]. Trick: Since \[\theta =\frac{\pi }{4}\] satisfies the equation and therefore the general value should be\[2n\pi \pm \frac{\pi }{4}\].
You need to login to perform this action.
You will be redirected in
3 sec
