wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Evaluate:
cos4(π8)+cos4(3π8)+cos4(5π8)+cos4(7π8)

Open in App
Solution

Let A=cos4(π8)+cos4(3π8)+cos4(5π8)+cos4(7π8)

cos4(5π8)=cos4(π2+π8)=sin4(π8)

cos4(7π8)=cos4(π2+3π8)=sin4(3π8)

A=cos4(π8)+cos4(3π8)+sin4(π8)+sin4(3π8)

Let's write in the form, (a+b)2=a2+2ab+b2

=(sin2(π8)+cos2(π8))2+(sin2(3π8)+cos2(3π8))22sin2(π8)cos2(π8)2sin2(3π8)cos2(3π8)

=1+112sin2π412sin23π4 .................. [sin2x=2sinxcosx] and [sin²θ+cos²θ=1]

=212(12+12)=212=32


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Property 3
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon