wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
Question

Prove that tan[π4+12cos1ab]+tan[π412cos1ab] = 2ba

Open in App
Solution

The LHS part of the equation is:
tan[π4+12cos1ab]+tan[π412cos1ab]letcos1ab=xcosx=abtan[π4+x2]+tan[π4x2]
=tanπ4+tanx21tanπ4tanx2+tanπ4tanx21+tanπ4.tanx2=1+tanx21tanx2+1tanx21+tanx2
=(1+tanx2)2+(1tanx2)2(1tanx2)(1+tanx2)=2(1+tan2x2)1tan2x2
=2cosx[since cos 2x=1tan2x21+tan2x2]
=2ba

flag
Suggest Corrections
thumbs-up
3
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Multiple and Sub Multiple Angles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon