Question

15. If tanα=1/2 and tanβ =1/3 then the value of α + β is

Answer 1

tanα=1/2

tanβ=1/3

Now, tan(α+β)=tanα+tanβ/1-tanα.tanβ

=1/2+1/3 / 1- 1/2.1/3

=5/6 / 1- 1/6

=5/6 / 5/6

=1

tan(α+β)=1

(α+β)=45°

Answer 2

Answer:

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

• π/4 is the right answer.