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[rah2]

a)\(\displaystyle{ sin2x+cosx=0}\)
b)\(\displaystyle{ 2cos^{2}(3x+Pi)=1}\)
c)\(\displaystyle{ |tg(x- \frac{pi}{3})|= \frac{ \sqrt{2} }{2}}\)
d)\(\displaystyle{ sinx-cosx=1}\)
e)\(\displaystyle{ cos2x-5cosx=0}\)
f)\(\displaystyle{ 5cos^{2}x+7sin^{2}x=6}\)

[lionek]

a)
\(\displaystyle{ sin2 \alpha +cos \alpha =0}\)
\(\displaystyle{ 2sin \alpha cos \alpha +cos \alpha =0}\)
\(\displaystyle{ cos \alpha(2sin \alpha +1)=0}\)
\(\displaystyle{ cos \alpha =0}\)
\(\displaystyle{ sin \alpha =- \frac{1}{2}}\)
b)
\(\displaystyle{ 2cos^2(\pi+3x)=1}\)
\(\displaystyle{ -2cos^2 3x=1}\)
\(\displaystyle{ cos^2 3x=- \frac{1}{2}}\)
\(\displaystyle{ cos3x=- \frac{ \sqrt{2} }{2}}\)
d)
\(\displaystyle{ sinx-cosx=1}\)
\(\displaystyle{ sin^2 x-cos^2 x- 2sinxcosx=1}\)
\(\displaystyle{ -2sinxcosx=0}\)
\(\displaystyle{ sinxcosx=0}\)
\(\displaystyle{ sinx=0}\)
\(\displaystyle{ cosx=0}\)
e)
\(\displaystyle{ cos2x-5cosx=0}\)
\(\displaystyle{ 2cos^2 x-1-5cosx=0}\)
\(\displaystyle{ 2cos^2 x-5cosx-1=0}\)
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f)
\(\displaystyle{ 5cos^{2}x+7sin^{2}x=6}\)
\(\displaystyle{ 5-5sin^2 x+7sin^2 x=6}\)
\(\displaystyle{ 2sin^2 x-1=0}\)
\(\displaystyle{ sin^2 x= \frac{1}{2}}\)
\(\displaystyle{ sinx= \frac{ \sqrt{2} }{2}}\)