Question

Sin^2x/cos^2 + sinxcscx = sec^2x Identify it, please explain so I know how you did it, thanks

Answer 1

to the risk of sounding redundant.

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Answer 2

let s=sin(x), c=cos(x)

s^2/c^2+s*csc(x)

=s^2/c^2+s/s (csc(x) = 1/sin(x), by definition of csc(x) )

=s^2/c^2+1

=s^2/c^2 + c^2/c^2

=(s^2+c^2)/c^2 (s^2+c^2=1, an identity)

=1/c^2

= sec^2(x) (by definition of sec(x) = 1/cos(x) )