A) \[\sqrt{2}\cos \theta \]
B) \[\sqrt{2}sin\theta \]
C) \[cos\theta \]
D) None of these
Correct Answer: B
Solution :
(b): \[{{(cos\theta +sin\theta )}^{2}}+{{(cos\theta -sin\theta )}^{2}}={{\cos }^{2}}\theta +\]\[{{\sin }^{2}}\theta +2\cos \theta \sin \theta +{{\cos }^{2}}\theta +{{\sin }^{2}}\theta -2\cos \theta \sin \theta \] \[\Rightarrow \] \[{{\left( \sqrt{2}\cos \theta \right)}^{2}}+{{\left( \cos \theta -\sin \theta \right)}^{2}}=1+1\] \[\Rightarrow \] \[2\,{{\cos }^{2}}\theta +{{(cos\theta -sin\theta )}^{2}}=2\] \[\Rightarrow \] \[{{(cos\,\theta -sin\theta )}^{2}}=2-2\,{{\cos }^{2}}\theta \] \[\Rightarrow \]\[{{(cos\theta -sin\theta )}^{2}}=2{{\sin }^{2}}\theta \] \[\Rightarrow \]\[\cos \theta -\sin \theta =\sqrt{2}\sin \theta \]
You need to login to perform this action.
You will be redirected in
3 sec
