Question

23. If A + B + C = π/2, then what is the
value of nan A tan B + tan B tan c +
tan C tan A ​

Answer 1

Answer:

If A + B + C = π/2, then tan A tan B + tan B tan c +  tan C tan A = 1​

Step-by-step explanation:

A + B + C = π/2

⇒ A + B = π/2 - C

⇒ tan(A+B) = tan( π/2 - C)

⇒ tanA + tanB/ 1 - tanA. tanB = cotC

⇒ tanA + tanB/ 1 - tanA. tanB = 1/tanC

⇒ tanC ( tanA + tanB ) = 1 - tanA. tanB

⇒ tan A tan B + tan B tan c +  tan C tan A = 1

Therefore, Answer will be 1.

Answer 2

The value of Tan A Tan B + Tan B Tan C + Tan A Tan C is 1  .

Step-by-step explanation:

Given as :

A + B + C = $\dfrac{\pi }{2}$

The value of Tan A Tan B + Tan B Tan C +  Tan C Tan A ​

According to question

∵  A + B + C = $\dfrac{\pi }{2}$

  A + B = $\dfrac{\pi }{2}$ - C

Taking Tan both side

Tan (A + B) = Tan ($\dfrac{\pi }{2}$ - C )

$\dfrac{Tan A + Tan B}{1-Tan A Tan B}$ = Cot C

$\dfrac{Tan A + Tan B}{1-Tan A Tan B}$ =  $\dfrac{1}{TanC}$

Cross multiplication

Or,   Tan C ( Tan A + Tan B ) = 1 - Tan A Tan B

Or,  Tan C Tan B + Tan B Tan C = 1 - Tan A Tan B

So,  Tan C Tan B + Tan B Tan C + Tan A Tan B = 1

Hence, The value of Tan A Tan B + Tan B Tan C + Tan A Tan C is 1  . Answer