Question

$if \: 0 \leqslant \alpha \: and \: \: \: \beta \leqslant 90 \: and \: \tan( \alpha + \beta ) = 3 \: and \: \tan( \alpha - \beta ) = 2 \: then \: value \: of \: \sin(2 \alpha )$
Please solve this problem.​

Answer 1

Answer:

1/√2

Step-by-step explanation:

Given tan(α+β)=3,tan(α−β)=2

tan2α=tan((α+β)+(α−β))=

{ tan(α+β)+tan(α−β)} / 1+tan(α+β)tan(α−β)

= (3+2) / 1−(3)(2)

=−1

As 0≤α≤90 ⟹0≤2α≤180

⟹2α=135

sin2α=sin135 = 1/√2

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