if triangle abc ,cosA.cosB+sinA.sinC=1 show that a:b:c=1:1:√2
if triangle abc ,cosA.cosB+sinA.sinC=1 show that a:b:c=1:1:√2
sumit suman , 9 Years ago
Grade 12th pass
Algebra> if triangle abc ,cosA.cosB+sinA.sinC=1 sh...
1 AnswersVikas TU
This ithe pure identity.
Take LHS and write them in other form that is:
cosA.cosB+sinA.sinC=1
cos(A+B) + cos(A-B) +cos(A-B) – cos(A+B) = 2
2cos(A-B) = 2
Cos(A-B) = 1
A-B = 0
A= B
Hence two angles are same the triangle is isscoeles.
And therfore two sides opposite to that angle would be same too.
Hence they both would share equal side ratio.
And soothes the ratio 1:1:root(2)
And therfore two sides opposite to that angle would be same too.
Hence they both would share equal side ratio.
And soothes the ratio 1:1:root(2)
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