Question

If tan-Atan B + tanB tan-C + tanºC tanA+ 2tan A tan-B tan-C = 1. then sin2A tanA + sin2B tanB + sin 2C Tan C = а) 0 b) І c) 2 d) 3 ​

Answer 1

Step-by-step explanation:





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Class 11

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>>Trigonometric Functions of Sum and Difference of Two angles

>>If in a triangle ABC,tan A ...

Question



If in a triangle ABC,tanA+tanB+tanC=6 and tanAtanB=2, then the triangle is:

A

right angled

B

obtuse angled

C

acute angled

D

isosceles

Medium

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Solution



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Correct option is

C

acute angled

A+B+C=180A+B=180−Ctan(A+B)=−tanC(1−tanAtanB)(tanA+tanB)=−tanCtanA+tanB+tanC=tanAtanBtanC=6

Now, tanC=3. So, the angle C is acute.

tanA+tanB=3