If A,B,C be the angles of a triangle, then ∑cotA+cotBtanA+tanB
1
2
-1
-2
Explanation for the correct option:
Step 1: Find the value of ∑cotA+cotBtanA+tanB
Given that, A,B,C are the angles of a triangle.
⟹A+B+C=180°
⟹tanA+tanB+tanC=tanAtanBtanC
cotA+cotBtanA+tanB=1tanA+1tanBtanA+tanB=(tanB+tanA)tanAtanBtanA+tanB=1tanAtanB
Step 2: Find the value of ∑cotA+cotBtanA+tanB
∑cotA+cotBtanA+tanB=1tanAtanB+1tanBtanC+1tanCtanA=tanC+tanA+tanBtanAtanBtanC=tanA+tanB+tanCtanAtanBtanC=tanAtanBtanCtanAtanBtanC=1
Hence the value of ∑cotA+cotBtanA+tanB is 1.
Hence option (A) is the correct option.