Question

Daca tgα=2,atunci sa se calculeze sin 2α, cos 2α, tg 2α.

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Answer 1

Notand tg $\frac{ \alpha }2}=t$, avem formulele sin$\alpha = \frac{2t}{1+t^2},cos \alpha = \frac{1-t^2}{1+t^2},si,tg \alpha = \frac{2t}{1-t^2},$, notand tgα=t, folosim aceleas formule pentru sin2α, cos2α, si tg2α, deoarece tgα=t=2, vom avea: $sin2 \alpha= \frac{2*2}{1+2^2}= \frac{4}{5};cos2 \alpha = \frac{1-2^2}{1+2^2}= \frac{-3}{5},si,tg2 \alpha = \frac{2*2}{1-2^2}= \frac{4}{-3}=- \frac{4}{3}$