Question

1 + sin 2x - sin x = cosx

Answer 1

1 + sin 2x - sin x = cosx

sin^2x + 2sinxcosx+ cos^2x  - sinx - cosx = 0

(sinx + cosx)^2 - (sinx + cosx) = 0

(sinx + cosx)*(sinx + cosx - 1)=0

 

1) sin x + cos x = 0

tgx + 1 =0

tgx = -1

x= - pi/4+pik, k∈Z

 

2) sinx + cosx = 1

√2*sin(pi/4 + x)= 1

sin(pi/4 + x)= √2/2

 

pi/4+x=pi/4+2pik

x=pi/4-pi/4+2pik

x=2pik, k∈Z

 

pi/4+x=3pi/4+2pik

x=3pi/4-pi/4+2pik

x=pi/2+2pik, k∈Z