If α = c o s - 1 3 5 , β = t a n - 1 1 3 , where 0 < α , β < π 2 , then α - β is equal to

α = c o s - 1 3 5 = t a n - 1 4 3 ∴ a - β = t a n - 1 4 3 - t a n - 1 1 3 = t a n - 1 4 3 - 1 3 1 + 4 3 × 1 3 = t a n - 1 1 13 9 = t a n - 1 9 13 = sin - 1 ⁡ 9 5 10

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Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

MathematicsInverse Trigonometric FunctionsSum And Difference Of AnglesMedium2 minPYQ_2019

MathematicsMediumsingle choice

If $α = {c o s}^{- 1} (\frac{3}{5})$ , $β = {t a n}^{- 1} (\frac{1}{3})$ , where $0 < α, β < \frac{π}{2},$ then $α - β$ is equal to

Options:

Answer:

Solution:

$α = {c o s}^{- 1} \frac{3}{5} = {t a n}^{- 1} \frac{4}{3}$
$∴ a - β = {t a n}^{- 1} \frac{4}{3} - {t a n}^{- 1} \frac{1}{3}$
$= {t a n}^{- 1} \frac{\frac{4}{3} - \frac{1}{3}}{1 + \frac{4}{3} \times \frac{1}{3}}$
$= {t a n}^{- 1} \frac{1}{\frac{13}{9}}$
$= t a n^{- 1} \frac{9}{13}$

$= \sin^{- 1} (\frac{9}{5 \sqrt{10}})$

Stream:JEESubject:MathematicsTopic:Inverse Trigonometric FunctionsSubtopic:Sum And Difference Of Angles

⏱ 2mℹ️ Source: PYQ_2019

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