Question

If α = cos⁻¹(3/5), β = tan⁻¹(1/3), where 0 < α, β < π/2 then (α - β) is equal to:
(A) sin⁻¹(9/5√10)
(B) cos⁻¹(9/5√10)
(C) tan⁻¹(9/5√10)
(D) tan⁻¹(9/14)

Answer 1

${\red{\huge{\underline{\mathbb{Given :-}}}}}$

α = cos⁻¹(3/5), β = tan⁻¹(1/3)

where 0 < α, β < π/2

${\purple{\huge{\underline{\mathbb{Answer:-}}}}}$

α = cos⁻¹(3/5)

↪ α = tan⁻¹(4/3)

α - β = tan⁻¹(4/3)- tan⁻¹(1/3)

we know that

$\tan {}^{ - 1} (x) - \tan {}^{ - 1} (y) = \tan {}^{ - 1} ( \frac{x - y}{1 + xy} )$

use this forumla

$\alpha - \beta = \tan {}^{ - 1} ( \frac{ \frac{4}{3} - \frac{1}{3} }{1 + \frac{4}{3} \times \frac{1}{3} } )$

α - β = tan⁻¹(9/13)

convert tan inverse term in sin inverse

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

correct option a)

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Answer 2

Step-by-step explanation:

If α = cos⁻¹(3/5), β = tan⁻¹(1/3), where 0 < α, β < π/2 then (α - β) is equal to:

(A) sin⁻¹(9/5√10)

hope this helps you

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