0
2 cos * cos * -1 = 2cos(square) * -1 =cos(square) + cos(square) *-1 =1- sin(square) +cos(square) * -1 1 - 1 * -1 =0
[sin - cos + 1]/[sin + cos - 1] = [sin + 1]/cosiff [sin - cos + 1]*cos = [sin + 1]*[sin + cos - 1]iff sin*cos - cos^2 + cos = sin^2 + sin*cos - sin + sin + cos - 1
iff -cos^2 = sin^2 - 1
1 = sin^2 + cos^2, which is true,
cos(phi - 1) = cos(phi)cos(1) + sin(phi)sin(1)
Manipulate normally, noting:
(1 + cot x)² - 2 cot x = 1² + 2 cot x + cot² x - 2 cot x
= 1 + cot² x
= 1 + (cos x / sin x)²
= 1 + cos² x / sin² x
= 1 + cos² x / (1 - cos² x)
= ((1 - cos² x) + cos² x)/(1 - cos² x)
= 1/(1² - cos² x)
= 1/((1 + cos x)(1 - cos x))
= 1/(1 - cos x)/(1 + cos x)
QED.
sin2x / (1-cos x) = (1-cos2x) / (1-cos x) = (1-cos x)(1+cos x) / (1-cos x) = (1+cos x)
sin2x=1-cos2x as sin2x+cos2x=1
1-cos2x = (1-cos x)(1+cos x) as a2-b2=(a-b)(a+b)