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

cos276°+cos216°-cos76°cos16°=


A

-14

No worries! We‘ve got your back. Try BYJU‘S free classes today!
B

12

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

34

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
Solution

The correct option is D

34


Explanation for the correct option:

Simplify the series using Trigonometric identities

cos276°+cos216°-cos76°cos16°=12[2cos276°+2cos216°-2cos76°cos16°]=12[1+cos2×76°+1+cos2×16°-2cos76°cos16°][2cos2A=1+cos2A]=12[2+cos152°+cos32°-cos76°+16°-cos76°-16°][2cosAcosB=cosA+B+cosA-B]=12[2+2cos(152°+32°2)cos(152°-32°2)-cos92°-cos(60°)][cosC+cosD=2cosC+D2cosC-D2]=12[2+2cos(92°)cos(60°)-cos92°-cos(60°)]=12[2+2cos(92°)×12-cos92°-12)]=12[2+cos(92°)-cos92°-12)]=12[2-12]=12×32=34

Therefore, Option(D) is correct.


flag
Suggest Corrections
thumbs-up
4
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Properties of Conjugate of a Complex Number
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon