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

Find the common roots of the equations
cos2x+sin2x=cotx
and 2cos2x+cos22x=1

Open in App
Solution

cos2x+sin2x=cotx12sin2x+2sinx.cosx=cosxsinxsinx2sin3x+2sin2xcosx=cosxsinx(12sin2x)=cosx(12sin2x)12sin2x=0&sinxcosx=0sinx=±12&sinx=cosx,Sox=π4Now,2cos2x+cos2(2x)=1cos2(2x)=12cos2x=cos2xcos2x=1&cos2x=0x=π2andx=π4Hence,thecommonrootisπ4.

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