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if (sinA+sinB)=2 then (cosA+cosB)=? A and B less equal 0 to 90 degree

if (sinA+sinB)=2 then (cosA+cosB)=? A and B less equal 0 to 90 degree

Grade:12th pass

2 Answers

Faiz
107 Points
5 years ago
sinA + sinB = 2...Let cosA + cosB = x...Squaring and adding both the equations: -> 2 + 2 cos(A-B) = x² + 4 -> cos(A-B) = x²/2 + 1As A and B lie in[0°, 90°]…Cos(A-B) lies in [0,1]... -> x²/2 + 1 lies in [0,1]…As this expression camnot be greater than one and first term being a square, so x has to be zero...this gives cosA + cosB = 0...
Faiz
107 Points
5 years ago
You can also do this question in a short way...As A and B lie in [0°, 90°], which shows that sinA abd sinB lie in the interval [0,1]…As sinA + sinB = 2 can only be satisfied when both sinA and sinB be 1....hence corresponding cosines will be zero...this also gives cosA + cosB = 0 as answer.

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