NIMCET 2012 — Mathematics PYQ
NIMCET | Mathematics | 2012The value of cot−1(21)+cot−1(13)+cot−1(−8) is:
Choose the correct answer:
- A.
0
- B.
π
(Correct Answer) - C.
∞
- D.
π/2
π
Explanation
1. Converting to tan−1:
cot−1(21)=tan−1(211)
cot−1(13)=tan−1(131)
cot−1(−8)=π+tan−1(−81)=π−tan−1(81)
2. Adding the first two terms:
Using the formula tan−1(x)+tan−1(y)=tan−1(1−xyx+y):
tan−1(211)+tan−1(131)=tan−1(1−21×131211+131)
=tan−1(273273−127313+21)=tan−1(27234)
=tan−1(81)
3. Combining all terms:
Substitute the result back into the full expression:
[tan−1(81)]+[π−tan−1(81)]
=π
Correct Option:
(b) π
Explanation
1. Converting to tan−1:
cot−1(21)=tan−1(211)
cot−1(13)=tan−1(131)
cot−1(−8)=π+tan−1(−81)=π−tan−1(81)
2. Adding the first two terms:
Using the formula tan−1(x)+tan−1(y)=tan−1(1−xyx+y):
tan−1(211)+tan−1(131)=tan−1(1−21×131211+131)
=tan−1(273273−127313+21)=tan−1(27234)
=tan−1(81)
3. Combining all terms:
Substitute the result back into the full expression:
[tan−1(81)]+[π−tan−1(81)]
=π
Correct Option:
(b) π