Question

simplify the trigonometric expression .
anyone plz .

Answer 1

SIN^-1 X=THETA
 SQUARING ON Bin−1x=θ
⇒sinθ=x
⇒sin2θ=x2
⇒1−cos2θ=x2
⇒cos2θ=1−x2
⇒cosθ=±√1−x2
⇒θ=cos−1±√1−x2
Putting this,
cos(cos−1±√1−x2)
=±√1−x2

But sin−1x is, by definition, in [−π2,π2] so cos(sin−1x)≥0

so cos(sin−1x)=√1−x2

OTH SIDES

Answer 2

i hope it will help you