Question

2sin inverse 3/5 = tan inverse 24/7

Answer 1

 Let y= arcsin(3/5), then what this means is sin(y)= 3/5, using the fact that (sin(y))^2 + (cos(y))^2=1 we can obtain that cos(y) = 4/5 therefore tan(y) = 3/4 

now we use that tan(x+w) =[tan(x) + tan(w)] / [ 1 - tan(x) tan(w)] by taking x=w we see that 

tan(2x) = 2tan(x) / [ 1 - tan(x)^2] 

then tan(2y)= 2(3/4) / [1 - (3/4)^2] = 24/7 

then arctan (24/7) = 2y = 2 arcsin(3/5)