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Algebra Difficulty 2.5 Junior Find the answer

Given α∈(0,π)\alpha \in (0, \pi), and cos⁡α=−35\cos\alpha = -\frac{3}{5}, then tan⁡α=\tan\alpha =

Pick one

Solution

Since α∈(0,π)\alpha \in (0, \pi), and cos⁡α=−35\cos\alpha = -\frac{3}{5},

then tan⁡α=−1cos⁡2α−1=−1(−35)2−1=−43\tan\alpha = -\sqrt{\frac{1}{\cos^2\alpha} - 1} = -\sqrt{\frac{1}{\left(-\frac{3}{5}\right)^2} - 1} = -\frac{4}{3}.

Therefore, the correct option is D\boxed{D}.

This problem mainly tests the application of basic trigonometric identities for angles in the same quadrant, focusing on computational skills. It is considered a basic question.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.