Question

plz help: the expression cos4x cos3x+sin4x sin3x is equivalent to?

Answer 1

@thu1935

Answer 2

y = cos 3x + cos 4x + sin 3x + sin 4x
Use the 2 trig identities:
cos a + cos b = 2cos (a + b)/2*cos (a - b)/2 and
sin a + sin b = 2sin (a + b)/2*cos (a - b)/2
(a + b) = 7x, and (a - b) = x
cos 3x + cos 4x = 2*cos 7x/2*cos x/2
sin 3x + sin 4x = 2sin 7x/2*cos x/2
y = 2*cos (x/2)*(cos 7x/2 + sin 7x/2)
You still can transform the last sum by using the identity: sin a + cos a = V2*sin (a + Pi/4).

Answer 3

(cos 7x/2 + sin 7x/2) = V2*sin (7x/2 + Pi/4)
Finally, y = 2V2*cos (x/2)*(sin (7x/2 + Pi/4)
Now, you have 2 basic trig equations to solve, if needed.