If sin (α - β) = \(\frac{7}{25}\), sin (α + β) = \(\frac{4}{5}\), 0° < α, β <\(\frac{π}{4}\), then
find the value of tan2α.
Answer & explanation
Correct answer: option 4
tan(2α) = tan (α + β + α - β)
= \(\frac{tan(α+β) + tan(α-β)}{1 - tan(α + β) tan(α - β)}\) ......(i)
sin (α - β) = \(\frac{7}{25}\)
cos (α+β) = \(\frac{4}{5}\)
Now put in (i)
tan(2α) = \(\frac{\frac{4}{3} + \frac{7}{24}}{1 - \frac{7}{24} × \frac{3}{4}}\) = \(\frac{\frac{24}{25}}{\frac{25}{32}}\)
tan(2α) = \(\frac{25}{24}\) × \(\frac{32}{25}\) = \(\frac{4}{3}\)