1) To find the value of cosxcos(pi/2 - x) = 1, we will use the identity cos(A)cos(B) = (1/2) * (cos(A - B) + cos(A + B)).
Applying this identity to the given expression, we get: cosxcos(pi/2 - x) = (1/2)(cos(x + pi/2) + cos(x - pi/2)) = (1/2)*(0 + 0) = 0.
Therefore, cosx*cos(pi/2 - x) = 0, not 1.
2) To find the value of cos(5π/4), you need to remember the unit circle and the values of cosine at specific angles.
The angle 5π/4 is in the third quadrant of the unit circle, where cosine is negative. You can also determine this by recognizing that 5π/4 is equivalent to 225 degrees, which is in the third quadrant.
The value of cos(5π/4) = cos(225°) = cos(-135°) = -√2/2.
1) To find the value of cosxcos(pi/2 - x) = 1, we will use the identity cos(A)cos(B) = (1/2) * (cos(A - B) + cos(A + B)).
Applying this identity to the given expression, we get:
cosxcos(pi/2 - x) = (1/2)(cos(x + pi/2) + cos(x - pi/2)) = (1/2)*(0 + 0) = 0.
Therefore, cosx*cos(pi/2 - x) = 0, not 1.
2) To find the value of cos(5π/4), you need to remember the unit circle and the values of cosine at specific angles.
The angle 5π/4 is in the third quadrant of the unit circle, where cosine is negative.
You can also determine this by recognizing that 5π/4 is equivalent to 225 degrees, which is in the third quadrant.
The value of cos(5π/4) = cos(225°) = cos(-135°) = -√2/2.
Therefore, cos(5π/4) = -√2/2.