Question

please answer quickly and correctly please ​

Answer 1

Answer:

answer. 4) pi/4. is correct

$( \alpha + \beta ) = \frac{\pi}{4}$

Step-by-step explanation:

$\tan( \alpha ) = \frac{1}{2} \\ \\ \tan( \beta ) = \frac{1}{3} \\ \\ \tan(( \alpha + \beta )) = \frac{ \tan( \alpha ) + \tan( \beta ) }{1 - \tan( \alpha ) \tan( \beta ) } = \frac{ \frac{1}{2} + \frac{1}{3} }{1 - \frac{1}{2}. \frac{1}{3} } \\ \\ = \frac{5}{6} \times \frac{6}{5} \\ \\ = 1 \\ \\ therefore \: \: ( \alpha + \beta ) = \frac{\pi}{4}$

Answer 2

Given that tan theta =1/2 and Tanpi is =1/3
Then tan(theta+pi)= tan theta + tan pi /1-tan theta tan pi
1/2+1/3/1-1/2.1/3
3+2/6/6-1/6
In numerator and denominator 6 is cancelled
5/5 =1 tan ( theta + pi )= 1 then
Theta + pi = 45 degree means pi/4