CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Prove that:

cosA1+sinA+1+sinAcosA=2SecA


Open in App
Solution

To prove:

cosA1+sinA+1+sinAcosA=2SecA

Taking LHS

cosA1+sinA+1+sinAcosA

=(cosA)(cosA)+(1+sinA)(1+sinA)(1+sinA)(cosA) ( Taking LCM of denominator)

=cos2A+(1+sinA)2(1+sinA)cosA=cos2A+1+sin2A+2sinA(1+sinA)cosA

=2+2sinA(1+sinA)cosA (sin2A+cos2A=1)

=2(1+sinA)(1+sinA)cosA=2cosA=2SecA

=RHS

Hence, proved cosA1+sinA+1+sinAcosA=2SecA


flag
Suggest Corrections
thumbs-up
151
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Sine Rule
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon