if in triangle ABC a=6,b=3 and cos(A-B)=4/5 then its area is
if in triangle ABC a=6,b=3 and cos(A-B)=4/5 then its area is
HEMANTH , 8 Years ago
Grade 9
Trigonometry> if in triangle ABC a=6,b=3 and cos(A-B)=4...
1 Answers
Arun
Dear Hemant
cos (A-B) = (1 -tan²(A-B)/2)/(1+tan²(A-B)/2) = 4/5
On cross multiplication and then solving
tan²(A-B)/2 = 1/9
tan(A-B)/2 = 1/3
Hence
(a-b) cot(C/2)/(a+b) = 1/3
On solving
Cot(c/2) = 1
C/2 = 45°
C = 90°
Hence it is a right angle triangle
Now area = (1/2)*3*6 = 9 square units
Regards
Arun (askIITians forum expert)
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