# The last big toughy

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.

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.

#### Attachments

• sincos.txt
275 bytes · Views: 160
HallsofIvy
Homework Helper
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.

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!

Originally posted by 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.

how old are you buddy?

16 currently in grade 11. Why?

Originally posted by PrudensOptimus
how old are you buddy?

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

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*}

Originally posted by majinknight
16 currently in grade 11. Why?

lol which state are you in?

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

are you in the canadian school system?

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

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