Question

Choose the correct answer:
In triangle ABC, Angle C = 90°, then tan A+ tan B=
a) b^2/ac
b) a+b
c) a^2/bc
d) c^2/ab​

Answer 1

Step-by-step explanation:

We know, A + B + C = 180⁰.

and C = 90⁰.

So, A + B = 90⁰.

now, tan (A + B) = (tan A + tan B) / (1 - tan A * tan B)

so, for A = b = 90⁰; (tan A * tan B) = 1

Therefore, tan A + tan B

= (1 / tan B) + tan B

= (1 + tan^2 B) / tan B

= sec^2 B / tan B

= 1 / (sin B * cos B)

= (2 / sin 2B)

Similarly, it also can be proven that, tan A + tan B = (2 / sin 2A)

So, sin 2A = sin 2B

But, please don’t jump to conclusion that, 2A = 2B. Instead, actually it is 2A = (180⁰ - 2B).