Question

If tan α=1/2, tanβ =1/3find the value of α+β​

Answer 1

Answer:

4C+3T = 2100. Multiply the equation by 5 to get

20C+15T = 10500 …(1)

5C+2T = 1750. Multiply the equation by 4 to get

20C+8T = 7000 …(2)

Subtract (2) from (1) to get

7T =3500, or

T = 3500/7 = 500

From (2), 20C= 7000–8T = 7000–4000 = 3000, or

C = 3000/20 = 150

Each chair costs Rs.150 and each table, Rs.500. Answer.

Answer 2

Answer:

$→ \tan( \alpha ) = \frac{1}{2} \\→ \tan( \beta ) = \frac{1}{3} \\ → \tan( \alpha + \beta ) = \frac{ \tan( \alpha ) + \tan( \beta ) }{1 - \tan( \alpha ) \tan( \beta ) } \\ = \frac{ \frac{1}{2} + \frac{1}{3} }{1 - ( \frac{1}{2} \times \frac{1}{3}) } = \frac{ \frac{5}{6} }{1 - \frac{1}{6} } = \frac{ \frac{5}{6} }{ \frac{5}{6} } = 1 \\→ \tan( \alpha + \beta ) = 1 \\ (\alpha + \beta) = \tan^{ - 1} (1) \\ \boxed{( \alpha + \beta ) = \frac{\pi}{4} }✓$

• π/4 is the right answer.