4(sin 2x) + 3(cos 2x) = 5[sin (2x + a)] where a = Tan^-1 (4/3) ... Is this True or False?

Answer 1

if tan(a) = 4/3 then sin(a) = 4/5 and cos(a) = 3/5

sin(2x + a) = sin(2x)cos(a) + cos(2x)sin(a)
= 3/5sin(2x) + 4/5cos(2x)

So times 5 gives 5[sin (2x + a)] = 3(sin 2x) + 4(cos 2x)

unless I made a careless mistake, the coefficients are backwards.

Answer 2

It's so true man. ;)