## mathslover 3 years ago Find the value of : sin 47 (degrees) + sin 61 (degrees) - sin 11 (degrees) - sin 25 (degrees)

1. 1on1

set the calculator to degrees and start pressing buttons

2. mathslover

lol @1on1 , that's a shortcut but I do want to do that without *calculator*

3. 1on1

Sorry, that will require much more thought from me !

4. mathslover

No problem! @sasogeek any suggestions, if no then I have only 1 .

5. mathslover

Not suggestion but an idea infact.

6. sasogeek

use the calculator to find their actual values and do normal addition... that's if u want to do some work... if not, u may use the calculator to find the whole answer.

7. mathslover

hmn quite hard if calculator is not allowed.

8. sasogeek

earlier i thought it was sin(A+B)-sin(A-B) sort of question but it's not, direct solution with the calculator is the way forward :) unless u know those values off the top of ur head xD

9. mathslover

xD thanks though

10. sasogeek

i do not wish to confuse you, but you may want to read this, http://www.trans4mind.com/personal_development/mathematics/trigonometry/sumProductCosSin.htm#Sum_of_Sine_and_Cosine

11. Yahoo!

@mathslover Do u knw the Value of Sin18 and cos36

12. Yahoo!

SinA + SinB = 2Sin (A+B)/2 . Cos (A-B)/2...Use this

13. mathslover

@Yahoo! and @sasogeek this was my main idea.

14. mathslover

Let me try again to find out the answer through the formula of sina + sinb

15. mathslover

OK so if I remember the values of : cos 36 degrees and sin 18 degrees then I am getting cos 7 degrees.

16. mathslover

cos Here is it how I did that : $\large{\sin 47 + \sin 61 = 2 \sin 54 \cos 7 }$ ^that theta(s) are in degrees. similarly : $\large{-(\sin 11 + \sin 25) = -( 2\sin 18 \cos 7)}$ from the above we get : $$2\cos 7 ( \sin 54 - \sin 18 )$$ $$2\cos 7 ( 2\cos 36 \sin 18)$$ $$4\cos 7 (\frac{\sqrt{5}+1}{4} \times \frac{\sqrt{5}-1}{4})$$ $$\cos 7$$ That is it! Is it correct? @sasogeek @Yahoo!

17. Yahoo!

Yup...thats wat i also Got

18. Yahoo!

2Sin54.cos7 - 2sin18cos7 2cos7 ( sin54 - sin18) sin54 = cos 36 2cos7(cos36 - sin18) 2cos7( (sqrt5 + 1)/2 - (sqrt5-1)/2) = cos7

19. Yahoo!

Sorry 2cos7( (sqrt5 + 1)/4 - (sqrt5-1)/4)

20. mathslover

np, thanks a lot for your help yahoo.

21. Yahoo!

Welcome....)...

22. Yahoo!

To..Be honest..U Did All the Hard Work..)