The challenge trignometry question is: simplify sin⁡(80∘)+sin⁡(40∘) using trignometric identities. All the angle values are in degrees.This is what I did: Let a=40∘. So we have sin⁡(2a)+sin⁡(a). Using the formula for sin⁡(2a), I have,2sin⁡(a)cos⁡(a)+sin⁡(a)=sin⁡(40)(2cos⁡(40∘)+1)All I got was a big red mark through the question. I looked at co-functions and half-angles and couldn't find a solution that came out to something I could do without a calculator. Any thoughts?

Question

The challenge trignometry question is: simplify sin⁡(80∘)+sin⁡(40∘) using trignometric identities. All the angle values are in degrees.This is what I did: Let a=40∘. So we have sin⁡(2a)+sin⁡(a). Using the formula for sin⁡(2a), I have,2sin⁡(a)cos⁡(a)+sin⁡(a)=sin⁡(40)(2cos⁡(40∘)+1)All I got was a big red mark through the question. I looked at co-functions and half-angles and couldn&#039;t find a solution that came out to something I could do without a calculator. Any thoughts?

lilwhitelieyc · Accepted Answer

You may have been intended to writesin⁡(80)+sin⁡(40)=2sin⁡(80+402)cos⁡(80−402)=2sin⁡(60)cos⁡(20)=3cos⁡(20)but I don&#039;t have a nice value for cos⁡(20) and neither does Alpha, which finds about 0.93969. The first two terms of the Taylor series should be close, and if you know π2≈10 you can write cos⁡(20)≈1−12(π9)2≈1−10162≈1−116=0.9375 which is very close.