Please help me to prove that sec^2x*cscx/sec^2x+csc^2x=sin x?

Question

prove that sec square of x times cscx divided by sec square of x plus csc square of x equals to sinx

Answer 1

for quick notation let s= sec, s2=sec2, c = csc , c2=csx2

(s2 c) / (s2 + c2) = sin

s2 c = sin (s2 +c2)

(1/cos2) (1/sin) = sin [(1/cos2) + (1/sin2) ] = (sin/cos2) + (1/sin)

multiply both sides by cos

(1/cos) (1/sin) = (sin/cos) + (cos/sin)

1/(cos sin) = (sin/cos) + (cos/sin)

multiply both sides by sinx cosx

1 = sin^2x + cos^2x

1 = 1

Answer 2

sec x = 1/sin x and csc x=1/ cos x

sec^2 x / sec^2 x = 1 so the above reduces to

csc x + csc^2 x = sin x not necessarily true.