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If sec(theta+alpha) + sec(theta-alpha)=2sectheta prove that cos theta= 2^1/2 cosalpha/2
one year ago

Arun
24739 Points

Dear student

sec(θ+α)+sec(θα)=2sec(θ) can be written as

1cos(θ+α)+1cos(θα)=2cosθ

or cos(θ+α)+cos(θα)cos(θ+α)cos(θα)=2cos(θ)

or2×2cosθcosαcos(θ+α+θα)+cos(θ+αθ+α)=2cosθ

or 2cosθcosαcos2θ+cos2α=1cosθ

or 2cos2θcosα=cos2θ+cos2α

or 2cos2θcosα=2cos2θ1+2cos2α1

or 2cos2θ(cosα1)=2cos2α2

or cos2θ=cos2α1cosα1=cosα+1

or cos2θ=2cos2(α2)

and cosθ=2cos(α2)

Hope it helps

one year ago
Saurabh Koranglekar
8387 Points

one year ago
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### Course Features

• 31 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions