Find the value of #sin(sec^(-1)(u/2))#?

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Answer 1 · 2017-03-30T05:16:58

#sin(sec^(-1)(u/2))=1/usqrt(u^2-4)#

Let #sec^(-1)(u/2)=x#, then

#secx=u/2# and #cosx=2/u#

Therefore #sinx=sqrt(1-cos^2x)#

= #sqrt(1-(2/u)^2)#

= #sqrt(1-4/u^2)#

= #sqrt((u^2-4)/u^2)#

= #1/usqrt(u^2-4)#

Now #sinx=1/usqrt(u^2-4)#, but #x=sec^(-1)(u/2)#

Hence #sin(sec^(-1)(u/2))=1/usqrt(u^2-4)#