Let (α + β) = 4/5 and let (α - β) = 5/13 , where 0 ≤ α, β ≤ π/4 , then 2α = - Mathematics MCQ AIEEE 2026 | ExamTest.live

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Let cos (α + β) = \frac{4}{5} and let sin (α - β) = \frac{5}{13}, where 0 \leq α, β \leq \frac{π}{4}, then tan 2 α =

Solution & Step-by-step Explanation

Given cos (α + β) = 4/5 ⟹ tan (α + β) = 3/4 (since α + β is in 1st quadrant).Given sin (α - β) = 5/13 ⟹ tan (α - β) = 5/12 .We need tan 2 α = tan ((α + β) + (α - β)) . tan 2 α = \frac{tan ( α + β ) + tan ( α - β )}{1 - tan ( α + β ) tan ( α - β )} tan 2 α = \frac{3/4 + 5/12}{1 - ( 3/4 ) ( 5/12 )} = \frac{( 9 + 5 ) /12}{1 - 15/48} = \frac{14/12}{33/48} tan 2 α = \frac{14}{12} \times \frac{48}{33} = \frac{14 \times 4}{33} = \frac{56}{33}

Try it yourself before checking the explanation above.

Let cos (α + β) = \frac{4}{5} and let sin (α - β) = \frac{5}{13}, where 0 \leq α, β \leq \frac{π}{4}, then tan 2 α =

\frac{56}{33}

\frac{19}{12}

\frac{20}{7}

\frac{25}{16}

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