Q. 124.2( 13 Votes )

If cosα + cosβ =

Answer :

To Prove: cos 2α + cos 2β = –2cos (α + β)


Given,


cosα + cosβ = 0 = sinα + sinβ …(1)


LHS = cos 2α + cos 2β


We know that: cos 2x = cos2x – sin2x


LHS = cos2α – sin2α + (cos2β – sin2β)


LHS = cos2α + cos2β – (sin2α + sin2β)


a2 + b2 = (a+b)2 – 2ab


LHS = (cosα + cosβ)2 – 2cosα cosβ –(sinα + sinβ)2 +2sinα sinβ


LHS = 0 - 2cosα cosβ -0 + 2sinα sinβ {using equation 1}


LHS = -2(cosα cosβ – sinα sinβ)


cos (α + β) = cosα cosβ – sinα sinβ


LHS = -2 cos (α + β) = RHS


Hence, cos 2α + cos 2β = –2cos (α + β)


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Prove that:
</
RD Sharma - Mathematics

Prove that:
</
RD Sharma - Mathematics

Prove that:
</
RD Sharma - Mathematics

Prove that:
</
RD Sharma - Mathematics

Prove that:
</
RD Sharma - Mathematics

Prove that:
</
RD Sharma - Mathematics

Prove that:
</
RD Sharma - Mathematics

Prove that:
</
RD Sharma - Mathematics

Mark the Correct RD Sharma - Mathematics

Mark the Correct RD Sharma - Mathematics