SOLUTION: simplify the following to a single trigonometry term 1. cos 10 . cos 340 - sin 190 . sin 200 ----------- ----------- ------ sin 10 . sin 70 + sin 100 . sin 20 2.

Algebra ->  Trigonometry-basics -> SOLUTION: simplify the following to a single trigonometry term 1. cos 10 . cos 340 - sin 190 . sin 200 ----------- ----------- ------ sin 10 . sin 70 + sin 100 . sin 20 2.       Log On


   

Question 1072509: simplify the following to a single trigonometry term
1. cos 10 . cos 340 - sin 190 . sin 200
------------------------------
sin 10 . sin 70 + sin 100 . sin 20

2. -cos ( 360 -x) tan ^2 x
--------------------
sin (x-180)cos(90+x)
Answer by MaxWong(38) About Me  (Show Source):
You can put this solution on YOUR website!
1.
Numerator:
cos 10 cos 340 - sin 190 sin 200
= cos 10 cos 20 - sin 10 sin 20
= cos(10 + 20)
= cos 30
Denominator:
sin 10 sin 70 + sin 100 sin 20
= sin 10 cos 20 + cos 10 sin 20
= sin(10+20)
= sin 30
Therefore
cos 10 . cos 340 - sin 190 . sin 200 cos 30
------------------------------------ = ------ = cot 30
sin 10 . sin 70 + sin 100 . sin 20 sin 30