Simplify sin(x+y)/sinxcosy

Answer 1

We can simplify this expression by using the trigonometric identity

sin(a + b) = sin(a)cos(b) + cos(a)sin(b).

Substituting a = x and b = y, we have

sin(x + y) = sin(x)cos(y) + cos(x)sin(y).

Dividing both sides of the equation by sin(x)cos(y), we get

sin(x + y) / (sin(x)cos(y)) = (sin(x)cos(y) + cos(x)sin(y)) / (sin(x)cos(y)).

Now, we can cancel out sin(x)cos(y) in the numerator and denominator, giving us

(sin(x)cos(y) + cos(x)sin(y)) / (sin(x)cos(y)) = (sin(x)cos(y)) / (sin(x)cos(y)) = 1.

Therefore, the simplified expression is 1.