Równanie trygonometryczne
: 1 kwie 2009, o 20:45
cosx - sinx - 1 = 0
\(\displaystyle{ \cos x - \sin x = 1}\)
\(\displaystyle{ (\cos x - \sin x) ^{2} = 1 ^{2}}\)
\(\displaystyle{ \cos ^{2} x -2\sin x \cos x + \sin ^{2} x = 1}\)
\(\displaystyle{ \cos ^{2} x -2\sin x \cos x + \sin ^{2} x = \sin ^{2}x + \cos ^{2}x}\)
\(\displaystyle{ -2\sin x \cos x = 0}\)
\(\displaystyle{ -\sin 2x=0}\)
\(\displaystyle{ \sin 2x=0}\)
\(\displaystyle{ 2x=k \pi}\)
\(\displaystyle{ x= \frac{k \pi}{2} \wedge k \in C}\)