Question

limit x tends to 0 sinax/tanbx

Answer 1

lim x→0 sinax/tanbx

multiply and divide by ab x²
we get
lim x→0 abx²sinax/abx²tanx

Now we know that
lim x→0 sinax/ax = 1 and
lim x→0 bx/tanbx = 1

thus applying this we get

lim x→0 sinax/tanbx = a/b

Answer 2

lim x-->0 sinax/tanbx
lim x-->0 sinax × bx ×ax / tanbx × ax ×bx

so the formula of Lim x-->0 sinf(x)/f(x) = 1 and

tanf(x)/f(x) = 1 so you get a/b