Question

URGENT!!
Dacă t€[0,2π], astfel încât tg t + ctg t = 2, calculați sin 2t.
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Answer 1

$\text{tg}t+\text{ctg}t =\dfrac{\sin t}{\cos t}+\dfrac{\cos t}{\sin t} = \dfrac{\sin^2 t+\cos^2 t}{\sin t\cos t} =\\ \\ = \dfrac{1}{\sin t\cos t} = \dfrac{2}{2\sin t\cos t} = \dfrac{2}{\sin 2t} = 2 \\ \\ \Rightarrow \sin 2t = 1$