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.

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) (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
RELATED QUESTIONS
1+sin+cos/1+sin-cos=1+cos/sin (answered by ikleyn)

(1+sin+cos)/(1+sin-cos)=(1+cos)/sin (answered by richard1234)

Use an identity to easily find:... (answered by math-vortex)

Which of the following is correct? (a) cos(.1) < sin(.1) < sin(.1)cos(.1) (b)... (answered by jsmallt9)

Sin+cos=1,find sin-cos... (answered by richard1234)

solve; sin/cos... (answered by Boreal)

Prove : Cos*tan-sin^2= sin(1-sin) (answered by stanbon)

what is the value of the following function? cos(130�)cos(10�) + sin(10�) sin(130�). (answered by lwsshak3)

cos(2x+10)=sin(x+20) (answered by amarjeeth123,ikleyn,Edwin McCravy)