How do you simplify #sin(2sin^-1(10x))#?

Question

1734 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-10-28T08:35:16

#sin(2sin^(-1)10x)=20xsqrt(1-100x^2)#

Let #sin^(-1)10x=y#

then #siny=10x# and #cosy=sqrt(1-(10x)^2)=sqrt(1-100x^2)#

and #sin(2sin^(-1)10x)#

= #sin(2y)#

= #2sinycosy#

= #2xx10x xxsqrt(1-100x^2)#

= #20xsqrt(1-100x^2)#