Find the value of expression: `sin(2tan^(-1)(1/3))+cos(tan^(-1)2sqrt(2

1.	Find the value of expression: `sin(2tan^(-1)(1/3))+cos(tan^(-1)2sqrt(2))`
Answer» `2 tan^-1 x = sin^-1 (2x)/(1-x^2) ` & `tan^-1 x = cos^-1 (1/sqrt(1 + x^2))` now, `sin(2 tan^-1 (1/3)) + cos( tan^-1 2 sqrt2)` `2 tan^-1 (1/3) = sin^-1 ( ( 2 xx 1/3)/(1 + (1/3)^2)) = sin^-1(2/3 xx 9/10) = sin^-1 3/5` `tan^-1 ( 2 sqrt3) = cos^-1(1/sqrt(1 + 8))` `= cos^-1 1/3` now, equating `3/6 + 1/3 = (9+5)/15 = 14/15` Answer

Discussion

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