Cos(2x) = cos^2(x) - sin^2(x) - cos(x)
but sin^2(x) = 1 - cos^2(x)
cos(2x) - cos(x) = cos^2(x) - (1 - cos^2(x) ) - cos(x)
cos(2x) - cos(x) = cos^2(x) - 1 + cos^2(x) - cos(x)
cos(2x) - cos(x) = 2cos^2(x) - 1 - cos(x)
cos(2x) - cos(x) = (2cos(x) + 1)(cos(x) - 1)
I think this is what you have asked for.
They’re similar due to AAA, each triangle is 180 degrees. since both of the triangles had a degrees of 60 i imputed 67 to the left triangle and they both equal each other
The object should be placed 20/cm from the lens so as to form its real image on the screen
<h3>Mirror equation</h3>
The mirror equation is given according to the expression below;
1/f = 1/u + 1/v
where
f is the focal length
u is the object distance
v is the image distance
Given the following parameters
f = 5cm
v = 20cm
Required
object distance u
Substitute
1/5 = 1/u +1/20
1/u = 1/5-1/20
1/u = 3/20
u = 20/3 cm
Hence the object should be placed 20/cm from the lens so as to form its real image on the screen
Learn more on mirror equation here; brainly.com/question/27924393
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I'm ASSUMING this is a 45-45-90 right triangle and that DF is the hypotenuse.
With that said. Angle F = 45 means that angle = 45 and angle E = 90 degrees.
There is only one rule for 45-45-90 right triangles:
hypotenuse = √(2) * leg
Given the hyp = 16
16 = √(2) * leg
divide both sides by √(2)
16/√(2) = leg
Rationalize the denominator
16√(2)/(√(2)*√(2) =
(16√(2)) / 2 =
8√2
