Question

if tan α =1/2 and tan β=1/3 then α+ β
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Answer 1

Answer:

tan⁻¹ 1/2 + tan⁻ 1/3

Step-by-step explanation:

α = tan⁻¹ 1/2

β =  tan⁻ 1/3

α+ β =  tan⁻¹ 1/2 + tan⁻ 1/3

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.