Social networking sites, blogs, and online articles are instant sources of news for internet users globally. However, in the absence of strict regulations mandating the genuineness of every text on social media, it is probable that some of these texts are fake news or rumours. Their deceptive nature and ability to propagate instantly can have an adverse effect on society. This necessitates the need for more effective detection of fake news and rumours on the web. In this work, we annotate four fake news detection and rumour detection datasets with their emotion class labels using transfer learning. We show the correlation between the legitimacy of a text with its intrinsic emotion for fake news and rumour detection, and prove that even within the same emotion class, fake and real news are often represented differently, which can be used for improved feature extraction. Based on this, we propose a multi-task framework for fake news and rumour detection, predicting both the emotion and legitimacy of the text. We train a variety of deep learning models in single-task and multi-task settings for a more comprehensive comparison. We further analyze the performance of our multi-task approach for fake news detection in cross-domain settings to verify its efficacy for better generalization across datasets, and to verify that emotions act as a domain-independent feature. Experimental results verify that our multi-task models consistently outperform their single-task counterparts in terms of accuracy, precision, recall, and F1 score, both for in-domain and cross-domain settings. We also qualitatively analyze the difference in performance in single-task and multi-task learning models.