If α=cos^(-1)⁡〖(3/5),〗 β=tan^(-1)⁡〖(1/3),〗 where 0 lesTh α,β lesTh π/2, then α-β is equal to

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If α=cos^(-1)⁡〖(3/5),〗 β=tan^(-1)⁡〖(1/3),〗 where 0 lesTh α,β lesTh π/2, then α-β is equal to
(a) tan^(-1)⁡(9/(5√10)) (b) sin^(-1)⁡(9/(5√10))
(c) cos^(-1)⁡(9/(5√10)) (d) tan^(-1)⁡(9/14)
Ans: b
Sol.
Here α=cos^(-1)⁡(3/5) and β=tan^(-1)⁡(1/3)
⇒cos⁡〖α=3/5〗 and tan⁡〖β=1/3〗
⇒sin⁡〖α=4/5,sin⁡〖β=1/√10,cos⁡〖β=3/√10〗 〗 〗
Now, sin⁡〖(α-β)=sin⁡〖α cos⁡〖β-cos⁡〖α sin⁡β 〗 〗 〗 〗
=4/5×3/√10-3/5×1/√10=9/(5√10)
⇒α-β=sin^(-1)⁡(9/(5√10))

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