Step-by-step explanation:
Consider
⇛cos{(3π/4) + x} - cos{(3π/4) - x}
We know that
cos x - cos y = 2sin{(x+y)/2}sin{(x-y)/2}
By, using this identity, we get
= -2sin[{(3π/4) + x + (3π/4) - x}/2] sin [{(3π/4) + x - (3π/4) + x}/2]
= -2sin[{(3π/4) + (3π/4)}/2] sin {(x + x)/2}
= -2sin[{2*(3π/4)}/2] sin (2x/2)
= -2sin(3π/4) sinx
= -2sin{x-(π/3)} sinx
= -2sin (π/4)sinx
= -2 * (1/√2) * sinx
= -√(2) * √(2) * (1/√2) * sinx
= -√(2) sinx
= RHS.
Hence, the value of cos{(3π/4) + x} - cos{(3π/4) - x} = -√(2) sinx .
Please let me know if you have any other questions.
