Question

As we know tanx = sinx / cosx. Also, sin(-x) = -sinx and cos(-x) = cosx.

Problem:

So, how I will write sin(-x) / cosx. According to me, there are two ways:

1. -sinx / cosx = -tanx
2. sin(-x) / cos(-x) = tanx

I am very much confused on this. Help me to resolve it!

Answer 1

The first way is correct.

The negative sign cannot be taken out and cancelled.

the (-x) inside sin and cos means that you're flipping the graph horizontally (now reading from left to right) instead of meaning that the value of the thing is negative.

so sin(-x)/cos(-x) = tan(-x)

and since tan(-x) does not equal tan(x) (the tan graph is an odd function like sin, so tan(-x)=-tan(x)), sin(-x)/cos(x) is -tan(x).

I'm sorry if this sounds even more confusing aa. Feel free to ask me on points where you don't understand and I'll try my best to answer!