2sin²X - 2sinXcosX=1

Question

2sin²X - 2sinXcosX=1

Answer 1

Task/25148335
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2sin²x - 2sinxcosx=1 ;
- 2sinxcosx= 1 -2sin²x;  
* * * 1 - 2sin²x=cos²x+sin²x -2sin²x =cos²x-sin²x =cos2x * * *
-sin2x =cos2x ;
sin2x = -cos2x  || :cos2x≠ 0
tg2x = -1 
2x =  -π/4 +π*k , k∈ℤ

x=  -π/8 +(π/2)*k , k∈ℤ .

Answer 2

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2sin²X - 2sinXcosX=1 ⇔sin²X - 2sinXcosX-cos²X=0⇔ tg²X -2tgX -1 =0