You have the following expression:
To verify the identity, you have that the left side of the equation becomes:
(1 + cosx)(1 - cosx) = (1 - cos^2 x)
because of the product of an expression by its conjugate result in a difference of squares. Or simplfy by expanding the factors and simplying.
Next, you have:
1 - cos^2 x = sin^2 x
because the Pythagorean identity.
Then, the identity is verified.
Option C:
The equation which matches the graph above is y = 4x - 4.
Solution:
Take any two points on the graph of the line.
Let the points are (0, -4) and (1, 0).
Here,
Slope of the line:
m = 4
y-intercept of the line is the point where the line crosses at y-axis.
Here, the line crosses at y-axis is (0, -4).
y-intercept, (c) = -4
Equation of a line is
y = mx + c
y = 4x + (-4)
y = 4x - 4
The equation which matches the graph above is y = 4x - 4.
Option C is the correct answer.