If the sides of a triangle are 3, 5, and 7 and the smallest and greatest angles are α and β respectively, then 4(1-cosα)(1-cosβ) is equal to:
35
37
34
311
Explanation of correct answer.
It is given that,
a=3b=5c=7
Therefore,
cosA=cosα=b2+c2-a22bc=52+72-322×5×7=1314
Again,
cosC=cosβ=a2+b2-c22ab=32+52-722×3×5=-12
Now,
4(1-cosα)(1-cosβ)=4(1-1314)(1+12)=37
Hence, Option (B) is correct.