## Butterfly16 2 years ago Find an exact value. cos 15° Options: A) sqrt 6 + sqrt 2 / 4 B) - sqrt2 + sqrt 6 / 4 C) - sqrt2 - sqrt 6 / 4 D) - sqrt6 + 1 / 4

1. Butterfly16

A) $\frac{ \sqrt{6}+\sqrt{2} }{ 4 }$ B) $\frac{ -\sqrt{2} +\sqrt{6} }{ 4 }$ C) $\frac{ -\sqrt{2} - \sqrt{6} }{ 4 }$ D) $\frac{ -\sqrt{6} +1}{ 4 }$

2. amoodarya

cos(a-b)=cosa cosb + sina sin b you know? if ok cos (45-30)= cos45 cos 30 +sin 45 sin 30

3. Butterfly16

where did you get all the numebrs?

4. amoodarya

|dw:1357845575004:dw| I dont get what you mean !

5. Butterfly16

But its for cos 15° ?

6. amoodarya

It is an unknown angle you have to make it bu known angle

7. amoodarya

you know that formula? if yeah put the numbers in it you will have answer (a)

8. Butterfly16

I think I got it. Can you help with another?

9. klimenkov

Also, you can use $$\cos^2\frac x 2=\frac{1+\cos x}2$$.

10. Butterfly16

@klimenkov Can you help with this one, pelase? Write the expression as either the sine, cosine, or tangent of a single angle. $\cos(\frac{ \pi }{ 5 }) \cos(\frac{ \pi }{ 7 }) + \sin (\frac{ \pi }{ 5}) \sin (\frac{ \pi }{ 7 })$

11. amoodarya

as "klimenkov " says you can use that formula shuch the way i draw|dw:1357846727839:dw|

12. amoodarya

cos(π/5)cos(π/7)+sin(π/5)sin(π/7)=cos (π/5-π/7) by the formula AS i sayd before cos (a+b)= cos a cos b-sin a sin b

13. Butterfly16

so would the cos (a+b) be pi/5+pi/7?

14. klimenkov

No. It will be $$\cos(\frac\pi5-\frac\pi7)$$ as @amoodarya said. Hope you can do this subtraction.

15. amoodarya

no i think that you get it cos (a+b)= cos a cos b-sin a sin b cos (a-b)= cos a cos b+sin a sin b but 2pi/35 is unknown angle

16. Butterfly16

$\cos(\frac{ \pi }{ 5 }+\frac{ \pi }{ 7 })$ is 2pi/35? Can you show me how to fill in the formula? I think it'd make it easier for me.

17. amoodarya

cos (a-b)= cos a cos b+sin a sin b a=pi/5 b=pi/7

18. Butterfly16

cos (pi/5-pi/7)= cos (pi/5) cos (pi/7)+sin (pi/5) sin (pi/7) ?

19. klimenkov

Yes.

20. Butterfly16

21. klimenkov

No. The answer is $$\cos(\frac{2\pi}{35})$$.

22. Butterfly16

over 25?

23. klimenkov

No. Zoom in.

24. Butterfly16

That's what I said?

25. klimenkov

You said this without cosine.