Show that: `cos(2tan^(-1)(1/7))=sin(4tan^(-1)(1/3))`

1.	Show that: `cos(2tan^(-1)(1/7))=sin(4tan^(-1)(1/3))`
Answer» LHS=`cos(2 tan^-1 (1/7))` `cos(tan^-1((1/7)/(1-49)))` `= cos(tan^-1(27/48))` `= cos(cos^-1(24/25)) = 24/25`= LHs RHS= `sin(4tan^-1(1/3)` `= sin(2(2tan^-1(1/3)))` `= sin(2 tan^-1 ((2/3)/(1-1/9)))` `= sin(2 tan^-1 (3/4))` `= sin(sin^-1((2 xx3/4)/(1 + 9/16)))` `= 24/25= `RHS so, LHS=RHS hence proved

Discussion

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