If A+B=225°, then cotA1+cotAcotB1+cotB=
1
-1
0
12
Explanation for the correct option :
Step 1 : Expressing the given data:
Given A+B=225°
Taking " cot " on both sides, cot(A+B)=cot225°
⇒cotAcotB–1cotA+cotB=1 [∵cot(180°+45°)=cot45°=1]
⇒ cotAcotB–1=cotA+cotB
⇒ cotAcotB=1+cotA+cotB…..(i)
Step 2: Simplification of [cotA1+cotA][cotB1+cotB]
Now, cotA1+cotAcotB1+cotB=cotAcotB(1+cotB)(1+cotA)
=cotAcotB1+cotA+cotB+cotAcotB
=cotAcotBcotAcotB+cotAcotB
=cotAcotB2cotAcotB
[cotA1+cotA][cotB1+cotB]=12
Hence, option "D" is correct.
If A + B = 225∘, then cotA1+cotA. cotB1+cotB =
If a+b = 225, then cot a/(1 + cot a )*cot b/(1+cot b) =