Question

If sin (x – α) = k sin (x + α) express tan x in terms of k and α.

Answer 1

sin(x-a) = k sin(x+a)

sinxcosa - sinacosx = k { sinxcosa + sinacosx }

sinxcosa(1-k)  =  sinacosx (k+1)

tanx cota =  1+k/1-k

tanx = (1+k/1-k) tan a

Note : formula used :  sin(A+B) = sinA cosB + sinB cosA 

and sin(A-B) = sinA cosB - sinB cosA