Đáp án:
$a)0\\ b)\dfrac{1}{3}\\ c)2.$
Giải thích các bước giải:
$a)\tan 83^\circ-\cot 7^\circ\\ =\tan 83^\circ-\tan(90^\circ- 7^\circ)\\ =\tan 83^\circ-\tan 83^\circ\\ =0\\ b)\tan\alpha+\cot\alpha=3\\ \Leftrightarrow \dfrac{\sin\alpha}{\cos\alpha}+\dfrac{\cos\alpha}{\sin\alpha}=3\\ \Leftrightarrow \dfrac{\sin^2\alpha+\cos^2\alpha}{\cos\alpha.\sin\alpha}=3\\ \Leftrightarrow \dfrac{1}{\cos\alpha.\sin\alpha}=3\\ \Rightarrow \cos\alpha.\sin\alpha=\dfrac{1}{3}\\ c)\cos^220^\circ+\cos^240^\circ+\cos^250^\circ+\cos^270^\circ\\ =\cos^220^\circ+\cos^240^\circ+\sin^2(90^\circ-50^\circ)+\sin^2(90^\circ-70^\circ)\\ =\cos^220^\circ+\cos^240^\circ+\sin^240^\circ+\sin^220^\circ\\ =(\cos^220^\circ+\sin^220^\circ)+(\cos^240^\circ+\sin^240^\circ)\\ =1+1\\ =2.$
