Question

solve in R the equations :
cos(2x)=√2/2
cos(3x)=sin(2x)
tan^2(x)-((√3) +1)tan(x)+√3=0

Answer 1

1. cos 2x = V2/2 = cos Pi/4 , and = cos 7Pi/4
a)2x = Pi/4 --> x = Pi/2
b) 2x = Pi/4 -> x = 7Pi/8

2. cos 3x = sin 2x = cos (Pi/2 - 2x) , and = cos (2Pi - Pi/2 + 2x)
a) 3x = Pi/2 - 2x -> 5x = Pi/2 --> x = Pi/10
b) 3x = 3Pi/2 + 2x -> x = 3Pi/2