Let cos ( α + β ) = 5 4 and let sin ( α − β ) = 13 5 , where 0 ≤ α , β ≤ 4 π , then tan 2 α =

cos ( α + β ) = 5 4 sin ( α − β ) = 13 5 tan 2 α = tan ( α + β + α − β ) = 1 − 4 3 12 5 4 3 + 12 5 = 33 56 ⇒ tan ( α + β ) = 4 3 ⇒ tan ( α − β ) = 12 5

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MathematicsTrigonometric Ratios & IdentitiesBasic Identities & T RatiosEasy2 minPYQ_2010

MathematicsEasysingle choice

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 $tan 2 α =$

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$cos (α + β) = \frac{4}{5} sin (α - β) = \frac{5}{13} tan 2 α = tan (α + β + α - β) = \frac{\frac{3}{4} + \frac{5}{12}}{1 - \frac{3}{4} \frac{5}{12}} = \frac{56}{33} \Rightarrow tan (α + β) = \frac{3}{4} \Rightarrow tan (α - β) = \frac{5}{12}$

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Basic Identities & T Ratios

⏱ 2mℹ️ Source: PYQ_2010

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