`sin(cos^-1 (sqrt(5)/5))` Find the exact value of the expression. (Hint: Sketch a right triangle.)

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balajia | College Teacher | (Level 1) eNoter

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`sqrt(5)/5=1/sqrt(5)`

Taking adjacent as 1 and hypotenuse as `sqrt(5)` ,then the opposite will be `sqrt((sqrt5)^2-1)=2.`

`cos^-1(1/sqrt5)=sin^-1(2/sqrt5).`

`sin(cos^-1(1/sqrt5))=sin(sin^-1(2/sqrt5)) = 2/sqrt5 = 0.894`