Prove that:`2sin^(-1)3/5=tan^(-1)(24)/7`

1.	Prove that:`2sin^(-1)3/5=tan^(-1)(24)/7`
Answer» LHS=`2 sin^(-1)""(3)/(5)=2tan^(-1)""((3)/(5))/(sqrt(1-((3)/(5))^(2)))` `( :. sin^(-1)x=tan^(-1)"(x)/(sqrt(1-x^(2))))` `=2tan^(-1)""(3)/(4)=tan^(-1)""(2xx(3)/(4))/(1-((3)/(4))^(2))` `=tan^(-1)""(3//2)/(7//16)=tan^(-1)""((3)/(2)xx(16)/(7))` `=tan^(-1)""((24)/(7))`=RHS. Hence Proved.

Discussion

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