Find the value of cos11π/12?

2 Answers
Jun 12, 2018

14(2+6)

Explanation:

using the trigonometric identity

xcos(x+y)=cosxcosysinxsiny

note that 11π12=2π3+π4

cos(11π12)=cos(2π3+π4)

=cos(2π3)cos(π4)sin(2π3)sin(π4)

=cos(π3)cos(π4)sin(π3)sin(π4)

=(12×22)(32×22)

=2464=14(2+6)

Jun 12, 2018

2+32

Explanation:

cos(11π12)=cos(π12+12π12)=cos(π12+π)=
=cos(π12)=cos(π12)
Find cos(π12) by using trig identity:
2cos2a=1+cos2a.
In this case:
2cos2(π12)=1+cos(π6)=1+32=2+32
cos2(π12)=2+34
cos(π12)=2+32 (because cos(π12) is positive)
Finally,
cos(11π12)=cos(π12)=2+32
Check by calculator.
cos(11π12)=cos165=0.966
- 2+32=1.9322=0.966. Proved