# The last big toughy

1. Jan 4, 2004

### majinknight

Ok the last question on those pages of question is this and i have got stuck and cant figure it out. I need to show that (ds=degrees)
Sin(45ds+x) +cos(45ds+x) = sqaureroot2 cosx.
Ok so i did left side first and changed it to.
Sin45Cosy + Cos45Siny +Cos45Cosy - Sin45Siny
Now what i want to do is divide out the CosY and Sin Y but even if i do that it doesnt make square root two and i dont know what to do from there. Can you help me solve this last practise question.

2. Jan 4, 2004

### pnaj

They've given you a trig problem that includes the sine and cosine of
a special angle. That should prod you in the right direction. If not, look at the attached text file.

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3. Jan 4, 2004

### HallsofIvy

Staff Emeritus
What you are doing doesn't make a whole lot of sense. What is Y?

sin(45+ x)= sin(45)cos(x)+ cos(45)sin(x) and
cos(45+ x)= cos(45)cos(x)- sin(45)sin(x).

Do you know what sin(45) and cos(45) are?

Plug those into the two equations above and add.

4. Jan 4, 2004

### majinknight

Oh ok i get it, ya i thought of putting the 1/root2 in but wasnt sure how to go from there but i understand now. Thankyou so much!

5. Jan 4, 2004

### PrudensOptimus

how old are you buddy?

6. Jan 4, 2004

### majinknight

16 currently in grade 11. Why?

7. Jan 4, 2004

### Muzza

Re: Re: The last big toughy

Haven't you discovered the "Profile" button yet, buddy? :)

8. Jan 4, 2004

### Tron3k

Just testing out the "math typesetting" thing:

\begin{align*} \sin(45^\circ + x) &= \sin(45^\circ) \cos x + \cos(45^\circ) \sin x \\ &= \frac{\cos x}{\sqrt{2}} + \frac{\sin x}{\sqrt{2}} \\ &= \frac{\cos x + \sin x}{\sqrt{2}} \end{align*}

9. Jan 4, 2004

### PrudensOptimus

lol which state are you in?

10. Jan 4, 2004

### majinknight

Im in Ontario Canada. Its a province not a state.

11. Jan 8, 2004

### jake_at

are you in the canadian school system?

12. Jan 8, 2004

### majinknight

Yes i am, i am glad you are all so interested in me. I feel so special

13. Jan 9, 2004

### jake_at

heh, it sounded alot like one of our A-level questions, i was curious about it.