If c o s α + β = 3 5 , sin ⁡ ( α - β ) = 5 13 and 0 < α , β < π 4 , then tan ⁡ 2 α is equal to:

c o s α + β = 3 5 ⇒ t a n α + β = 4 3 s i n ( α - β ) = 5 13 ⇒ t a n ( α - β ) = 5 12 Now, t a n 2 α = t a n α + β + α - β = t a n ( α + β ) + t a n ( α - β ) 1 - t a n ( α + β ) t a n ( α - β ) = 4 3 + 5 12 1 - 4 3 × 5 12 = 63 16

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Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

MathematicsTrigonometric Ratios & IdentitiesAddition, Multiplication, Subtraction formula based,Multiple/Submultiple anglesEasy2 minPYQ_2019

MathematicsEasysingle choice

If $c o s (α + β) = \frac{3}{5}, \sin (α - β) = \frac{5}{13}$ and $0 < α, β < \frac{π}{4},$ then $\tan (2 α)$ is equal to:

Options:

Answer:

Solution:

$c o s (α + β) = \frac{3}{5} \Rightarrow t a n (α + β) = \frac{4}{3}$

$s i n (α - β) = \frac{5}{13} \Rightarrow t a n (α - β) = \frac{5}{12}$

Now,

$t a n 2 α = t a n ((α + β) + (α - β))$

$= \frac{t a n (α + β) + t a n (α - β)}{1 - t a n (α + β) t a n (α - β)}$

$= \frac{\frac{4}{3} + \frac{5}{12}}{1 - \frac{4}{3} \times \frac{5}{12}} = \frac{63}{16}$

Stream:JEESubject:MathematicsTopic:Trigonometric Ratios & IdentitiesSubtopic:Addition, Multiplication, Subtraction formula based,Multiple/Submultiple angles

⏱ 2mℹ️ Source: PYQ_2019

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