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If A+B+C=180o, then [(tanA+tanB+tanC)/(tanA tanB tanC)]=
  • a)
    0
  • b)
    2
  • c)
    1
  • d)
    -1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If A+B+C=180o, then [(tanA+tanB+tanC)/(tanA tanB tanC)]=a)0b)2c)1d)-1C...
Given, A + B + C = 180
So, A + B = 180 - C
Taking tan on both sides we get,
⇒ tan(A+B) = tan(180-C)
⇒ 
⇒ tanA + tanB = -tanC(1 - tanA tanB)
⇒ tanA + tanB = - tanC + tanA tanB tanC
⇒ tanA + tanB + tanC = tanA tanB tanC
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Most Upvoted Answer
If A+B+C=180o, then [(tanA+tanB+tanC)/(tanA tanB tanC)]=a)0b)2c)1d)-1C...
Given: A + B + C = 180°

To prove: [(tanA tanB tanC)/(tanA tanB tanC)] = 1

Proof:

1. Simplifying the given expression:

[(tanA tanB tanC)/(tanA tanB tanC)] = tanA tanB tanC / (tanA tanB tanC)

= 1

2. Using the fact that A + B + C = 180°:

tan(A + B + C) = tan 180°

Using the formula, tan(A + B + C) = (tanA + tanB + tanC - tanA tanB tanC)/(1 - tanA tanB - tanB tanC - tanC tanA)

On substituting the value of A + B + C = 180°, we get:

tan 180° = (tanA + tanB + tanC - tanA tanB tanC)/(1 - tanA tanB - tanB tanC - tanC tanA)

0 = tanA + tanB + tanC - tanA tanB tanC

tanA + tanB + tanC = tanA tanB tanC

Dividing both sides by tanA tanB tanC, we get:

1 = (tanA + tanB + tanC)/(tanA tanB tanC)

Substituting this value in the given expression, we get:

[(tanA tanB tanC)/(tanA tanB tanC)] = 1

Hence, the given expression is proved to be equal to 1.

Therefore, the correct answer is option C (1).
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Community Answer
If A+B+C=180o, then [(tanA+tanB+tanC)/(tanA tanB tanC)]=a)0b)2c)1d)-1C...
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If A+B+C=180o, then [(tanA+tanB+tanC)/(tanA tanB tanC)]=a)0b)2c)1d)-1Correct answer is option 'C'. Can you explain this answer?
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