Question

3cos(x+1)-4sin(x+1)=5

Answer 1

x+1=a
3cos²a/2-3sin²a/2-8sina/2cosa/2-5sin²a/2-5cos²a/2=0
8sin²a/2-8sina/2coa/2-2cos²a/2=0/2cos²a/2≠0
4tg²a/2-4tga/2-1=0
tga/2=m
4m²-4m-1=0
D=16+16=32
m1=(4-4√2)/8=0,5-0,5√2⇒tga/2=0,5-0,5√2⇒a/2=arctg(0,5-0,5√2)+πn⇒a=
=2arctg(0,5-0,5√2)+2πn⇒x+1=2arctg(0,5-0,5√2)+2πn⇒x=-1+2arctg(0,5-0,5√2)+2πn
m2=0,5-0,5√2⇒tga/2=0,5-0,5√2⇒a/2=arctg(0,5-0,5√2)+πn⇒a=
=2arctg(0,5+0,5√2)+2πn⇒x+1=2arctg(0,5+0,5√2)+2πn⇒x=-1+2arctg(0,5+0,5√2)+2πn