Question

If A = 35°, B = 15°, C = 40°, then
tan A.tan B+tan B. tan C+tanC.tan A=​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Given : A = 35°, B = 15°, C = 40°

To find : tan A.tan B+tan B. tan C+tanC.tan A

Step-by-step explanation:

taking

$\tan ((A+B)+C)= 35^\circ +15^\circ +40^\circ \\\\\tan ((A+B)+C)= \tan 90^\circ \\\\\frac{\tan (A+B)+\tan C}{1-\tan(A+B)\tan C}= \frac{1}{0}\\\\1-\tan(A+B)\tan C= 0 \\\\\tan(A+B)\tan C=1\\\\\left ( \frac{1\tanA+\tan B}{1-\tan A \tan B} \right )\tan C=1\\\\\tan A\tan C+\tan B \tan C = 1-\tan A \tan B \\\\\tan A \tan B+\tan B \tan C+\tan C \tan A = 1$

hence , the value is 1

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