Answer
a) False b) True c) True
Work Step by Step
a) $\dfrac{d}{d\theta}[\dfrac{\sec ^3 \theta}{3} +C]= \sec^2 \theta \sec \theta \tan \theta \ne \tan \theta \sec^2 \theta$; False
b) $\dfrac{d}{d\theta}[\dfrac{1}{2} \tan^2 \theta +C]= \dfrac{1}{2} (2 \sec^2 \theta \tan \theta) = \tan \theta \sec^2 \theta$; True
c) $\dfrac{d}{d\theta}[\dfrac{1}{2} \sec^2 \theta +C]= \dfrac{1}{2} (2 \sec \theta \sec \theta \tan \theta) = \tan \theta \sec^2 \theta$; True