How do you simplify # sin(tan^-1(1/2))#?

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Answer 1 · 2018-03-04T07:48:07

We can write as follows,

#sin(tan^-1(1/2)) =sin(sin^-1(1/(sqrt(5))))=1/sqrt(5)#

Answer 2 · 2018-03-04T07:48:18

The answer is #=1/sqrt5#

Let #theta=tan^-1(1/2)#

Then,

#tantheta=1/2#

We need,

#sin(tan^-1(1/2))=sintheta#

If #tan theta=1/2#,

#tan^2theta+1=1/cos^2theta#

#cos^2theta=4/5#

#sin^2theta=1-4/5=1/5#

#sintheta=1/sqrt5#