Answer
a) $\sqrt 2 \sin 2 \theta +\dfrac{\pi}{4}$
b) $\sqrt 2 \cos 2 \theta -\dfrac{\pi}{4}$
Work Step by Step
a) $\sqrt {(1)^2+ (1)^2} \sin 2 \theta + arctan (1)=\sqrt 2 \sin 2 \theta +\dfrac{\pi}{4}$
b) $\sqrt {(1)^2+ (1)^2} \cos 2 \theta - arctan (1)=\sqrt 2 \cos 2 \theta -\dfrac{\pi}{4}$
