How do you find the exact value of $Sin(arcsin(4/5)+arctan(12/5))$ ?

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Answer 1 · 2016-11-08T04:03:47

$Sin(arcsin(4/5)+arctan(12/5))$

$=Sin(arcsin(4/5)+arc cot(5/12))$

$=Sin(arcsin(4/5)+arc csc(sqrt(1+(5/12)^2)$

$=Sin(arcsin(4/5)+arc csc(13/12))$

$=Sin(arcsin(4/5)+arc sin(12/13))$

$=Sin(arcsin((4/5)xxsqrt(1-(12/13)^2)+(12/13)xxsqrt(1-(4/5)^2))$

$=(4/5xx5/13)+(12/13xx3/5)=56/65$

How do you find the exact value of Sin(arcsin(4/5)+arctan(12/5))Sin(arcsin(4/5)+arctan(12/5))?