How do you simplify \cos(\sin^{-1}x) ?

gorovogpg

gorovogpg

Answered question

2021-12-13

How do you simplify cos(sin1x) ?

Answer & Explanation

Matthew Rodriguez

Matthew Rodriguez

Beginner2021-12-14Added 32 answers

After using u=arcsin(x) or x=sin(u) transforms
cos(arcsinx)=cosu
=1(sinu)2
=1x2
sonSnubsreose6v

sonSnubsreose6v

Beginner2021-12-15Added 21 answers

cos(sin1x) 
Let sin1x=θ 
Then x=sinθ 
Place the value for x in cos(sin1x) 
cos(sin1(sinθ)) 
The resulting equation is, 
cosθ 
We have sin2θ+cos2θ=1 
cos2θ=1sin2θ 
cosθ=1sin2θ 
We have already found that x=sinθ, then x2=sin2θ. Now put x2 in the place for sin2θ 
cosθ=1x2

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