how to do this sum, please? (A Maths)

The equation 4cos(x + 45°) + ksin(x + 45°) = psinx holds for all values of x

Put x = - 45°, the equation becomes:
4cos(- 45° + 45°) + ksin(- 45° + 45°) = psin(- 45°)
4cos0°+ ksin0° = - psin45°
4 = - p /(√2)
p = - 4(√2) .............(1)

put x = 45°, the equation becomes:
4cos(45° + 45°) + ksin(45° + 45°) = psin45°
4cos90°+ ksin90°= psin45°
0 + k = p/(√2) .......................from (1): p = -4 (√2)
k = -4 (√2)/(√2)
k = - 4

Therefore, k = - 4 & p = - 4(√2)

2007-05-15 19:21:00 補充：
To select a value of x wisely would help us to simplify the equation & solve the equation. In general, choosing a value to "eliminate" one term with variable is a common method. e.g. put x = - 45°to eliminate the term ( ksin(x 45°) ) with variable k.