question_answer

For \[\mathbf{0{}^\circ }<\theta <\mathbf{90{}^\circ },\] if \[\sqrt{\mathbf{2}}\mathbf{(sin}\theta \mathbf{+cos}\theta \mathbf{)}\]\[=\mathbf{1+2 sin}\theta \mathbf{ cos}\theta \] then which among the following is not correct?

A)  \[Sin\text{ }\theta -cos\text{ }\theta =0\]                                    

B)  \[Sin\text{ }\theta +cos\text{ }\theta =0\]

C)  \[\theta =45{}^\circ \]                                                 

D)  \[Sin\text{ }2\theta =2\text{ }cos\left( \theta +15 \right)\]

E)  None of these