If , where , then α – β is equal to

Engineering

Mathematics

Basic of Inverse Trigonometric Functions

Question

If $α = \cos^{- 1} (\frac{3}{5}), β = \tan^{- 1} (\frac{1}{3})$ , where $0 < α, β < \frac{π}{2}$ , then α – β is equal to

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

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

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

$\tan^{- 1} (\frac{9}{14})$

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

$cosα = \frac{3}{5}, tanβ = \frac{1}{3}$

$\Rightarrow tanα = \frac{4}{3}$

$\Rightarrow \tan (α - β) = \frac{\frac{4}{3} - \frac{1}{3}}{1 + \frac{4}{3}, \frac{1}{3}} = \frac{9}{13}$

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