• 100% Satisfaction Guarantee
mhasan420, Master's Degree
Category: Math Homework
Satisfied Customers: 1849
Experience:  BA Maths, Oxford
30103992
Type Your Math Homework Question Here...
mhasan420 is online now

# find cos 105 degrees by using 105 degrees 60 degrees + 45 degrees -----------------------

### Resolved Question:

find cos 105 degrees by using 105 degrees=60 degrees + 45 degrees
----------------------------------------------------------------------------
simplify the given expression
sin pi/6 cos 2pi/3 + cos pi/6 sin 2pi/3
----------------------------------------------------------------------------
Find the exact value of the expression using radicals
sin 10 degrees cos 35 degrees + cos 10 degrees sin 35 degrees
----------------------------------------------------------------------------
Find the exact value of the expression
tan 25 degrees + tan 5 degrees over
1-tan 25 degrees tan 5 degrees
----------------------------------------------------------------------------
Submitted: 7 years ago.
Category: Math Homework
Expert:  mhasan420 replied 7 years ago.

Hi there!

1)

cos (105) = cos (60 + 45)

= cos 60 cos 45 - sin 60 sin 45

= (1/2)(1/√2) - (√3/2)(1/√2)

= (1/(2√2))(1- √3)

= (√2/4)(1-√3)

2)

sin pi/6 cos 2pi/3 + cos pi/6 sin 2pi/3

= (1/2)(-1/2) + (√3/2)(√3/2)

= -1/4 + 3/4

= 1/2

3)

sin 10 cos 35 + cos 10 sin 35

= sin (10+35)

= sin 45

= √2/2

4)

(tan 25 + tan 5)/(1-tan 25 tan 5)

= tan (25 + 5)

= tan 30

= 1/√3

= √3/3

Hopefully this helps. If your require further clarification do let me know. Otherwise, please do not forget to click 'Accept'. Thanks!

Edited by M Hasan on 2/23/2010 at 4:34 PM EST
Customer: replied 7 years ago.
for number 1 they said the answer is √2/4 - √6/4 how did they get that
Expert:  mhasan420 replied 7 years ago.

Hi,

You could further expand it out:

(√2/4)(1-√3) = √2/4 - (√2/4)(√3) = √2/4 - (√2√3)/4 = √2/4 - √6/4

Hope this helps. If you require further clarification do let me know. Otherwise, please do not forget to click 'Accept'. Thanks!