Triangles And Properties Of Triangle Question 1
Question: A, B, C are the angles of a triangle, then $ {{\sin }^{2}}A+{{\sin }^{2}}B+{{\sin }^{2}}C-2\cos A\cos B\cos C= $
Options:
A) 1
B) 2
C) 3
D) 4
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ {{\sin }^{2}}A+{{\sin }^{2}}B+{{\sin }^{2}}C $ $ =1-{{\cos }^{2}}A+1-{{\cos }^{2}}B+{{\sin }^{2}}C $ $ =2-{{\cos }^{2}}A-\cos (B+C)cos(B-C) $ $ =2-\cos A[cosA-cos(B-C)] $ $ =2-\cos A[-cos(B+C)-cos(B-C)] $ $ =2+\cos A.2\cos B\cos C $
$ \therefore {{\sin }^{2}}A+{{\sin }^{2}}B+{{\sin }^{2}}C-2\cos A\cos B\cos C=2 $
BETA
