Question

Show that sinx(cscx+sinxsec^2x)=sec^2x

Answer 1

sec(x)= 1/cos(x) ; csc(x)= 1/sin(x) ; sin(x)/cos(x) = tan(x) ; sin^2(x)+cos^2(x)=1 ( divided each side of this equation by cos^2(x) to get ) : tan^2(x) + 1 = sec^2(x)

sinX(cscX+sinX(sec^2 X)) =sec^2

sin(x)* (1/sin(x) + sin(x)*(1/cos^2(x)) = sec^2(x)

by multiplication

sin(x)/sin(x) + sin^2(x)/cos^2(x) = sec^2(x)

1+ tan^2(x)= sec^2(x) ----> this is an identity so we have solved the problem