Question

Решить уравнение tg2x=ctg5x

Answer 1

ctgx=1/tgx

tg2x-1/tg5x=0, cos2x≠0,  sin5x≠0  

tg2x * tg5x -1 

------------------ =0

    tg5x                  

sin2x    sin5x

------- * --------  -1=0

cos2x   cos5x          

sin2x *sin5x-cos2x *cos5x =0,   

-(cos2x *cos5x-sin2x *sin5x)=0, -cos(2x+5x)=0,  cos7x=0,  

7x=π+2πn,  x=π/7+2πn/7, n∈Z