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if sin α + sin β = a and cos α + cos β = b , then the value of coz ( α + β ) is

if sinα+sinβ=a and cosα+cosβ=b, then the value of coz(α+β) is 

Grade:11

3 Answers

Harshit Singh
askIITians Faculty 5963 Points
6 months ago
Dear Student

sinα+sinβ=a
on squaring
sin2α+sin2β+ 2 sinαsinβ=a2......(i)

cosα+cosβ=b
on squaring
cos2α+cos2β + 2.cosαcosβ=b2.....(ii)
Adding equation i and ii
sin2α+sin2β+ 2sinαsinβ+cos2α+cos2β + 2.cosαcosβ = a2 + b2
since sin2A + cos2A = 1
2 + 2(cosαcosβ+sinαsinβ) =a2+ b2
cos(α- β)=cosαcosβ+sinαsinβ= (a2+ b2–2)/2


Thanks
Ram Kushwah
110 Points
5 months ago
if sinα+sinβ=a and cosα+cosβ=b, then the value of coz(α+β) is
Dear Hiba Ismail,
Find the solution in the attached file
 
Ram Kushwah
110 Points
5 months ago
Dear student ,
Greeting of day
Please find attached the solution  in a image file,
I hope this will clear your doubts and will help in your study
Thanks
 

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