Question

Help?
Simplify the expression: cot x sin x - sin((pi/2)-x) + cos x.

Answer 1

@mathmale You busy?

Answer 2

Hello!
My first suggestion would be that you use the subtraction formula for the sine to simplify -sin ( (pi/2) - x).

If A and B are angles, the subtraction formula in question is

sin (A-B)=sin A cos B - cos A sin B.

Would you please apply this to simplify -sin ( (pi/2) - x).

Please recall that sin pi/2 = 1 and cos pi/2 = 0.

Answer 3

\[\cot x \sin x -\sin(\frac{ \pi }{ 2 }-x) +\cos x\]

Answer 4

Very glad you're using Equation Editor. Your work looks so neat!

sin( pi/2 - x) = cos x,

so -sin ( pi/2 - x ) = - cos x

so your expression becomes what?

Answer 5

So we get... \[\cot x \sin x -1-\cos x-\sin x\]
...Right?

Answer 6

How did you arrive at that 1 in the middle of your expression, and how ... that sinx at the end?

Answer 7

No, wait.. My bad. Hang on.

Answer 8

It's important that you simplify -sin ( pi/2 - x) first. Once you've done that, substitute the result into the original equation.

Answer 9

I think I did that because you said sin (A-B)=sin A cos B - cos A sin B. Then Please recall that sin pi/2 = 1 and cos pi/2 = 0. I just screwed up on the end...

Answer 10

So would it just be cot x sin x -cos x + cos x.. Well, cot x sin x?

Answer 11

Right. That whole mess simplifies to cot x sin x,
and even cot x sin x can be simplified. Try it. Hint: How is cot x defined?

Answer 12

It goes down to cos x, right?