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If tan–1 2, tan–13 are two angles of a triangle, then what is the third angle
  • a)
    tan–12
  • b)
    tan–14
  • c)
    π/4
  • d)
    π/3
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If tan1 2, tan13 are two angles of a triangle, then what is the third ...
**Solution:**

To solve this problem, we need to use the fact that the sum of the angles in a triangle is always 180 degrees.

Given that tan(12) and tan(13) are two angles of a triangle, let's assume that the third angle is x.

According to the tangent function, we know that tan(12) = tan(180 - 12) = tan(168) and tan(13) = tan(180 - 13) = tan(167).

We also know that tan(x) = tan(180 - (12 + 13)) = tan(155).

To find the value of tan(155), we can use the following identity:

tan(180 - x) = -tan(x)

Using this identity, we can rewrite tan(155) as:

tan(155) = -tan(25)

We know that tan(180 - 25) = tan(155), so we can rewrite tan(155) as:

tan(155) = -tan(180 - 25) = -tan(155)

Therefore, the third angle of the triangle is -tan(155).

Now let's look at the given options:

a) tan(12) - This is not equal to -tan(155), so it is not the correct answer.
b) tan(14) - This is not equal to -tan(155), so it is not the correct answer.
c) 4 - This is not equal to -tan(155), so it is not the correct answer.
d) 3 - This is not equal to -tan(155), so it is not the correct answer.

As none of the given options are equal to -tan(155), the correct answer is none of the above.

Therefore, the given question does not have a correct answer among the options provided.
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If tan1 2, tan13 are two angles of a triangle, then what is the third anglea)tan12b)tan14c)/4d)/3Correct answer is option 'C'. Can you explain this answer?
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