Question

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Sprawdź tożsamość

Answer 1

1/cos(x) - cos(x)/(1+sin(x)) = tg(x)

1/cos(x) - cos(x)/(1+sin(x)) = [(1+sin(x) - cos²(x))] / [cos(x)*(1+sin(x))] =

= [(sin²(x) + cos²(x) + sin(x) - cos²(x))] / cos(x)*(1+sin(x)) =

= [(sin²(x) + sin(x))] / [cos(x)*(1+sin(x))] =

= [sin(x)*(sin(x) + 1)]/[cos(x)*(1+sin(x))] = sin(x)/cos(x) = tg(x)