Question

Verify each trigonometric equation by substituting identities to match the right hand side of the equation to the left hand side of the equation.

1 + sec2x sin2x = sec2x

[(sin(x))/(1-cos(x))]+[(sin(x))/(1+cos(x))]=2csc(x)

Answer 1

The answer to the given equation above is that:

1+sec^2 x sin^2 x=sec^2 x

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

=cos^2 x/cos^2 x + sin^2 x/cos^2 x = 1/cos^2 x

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

multiply both sides by cos^2 x cos^2x + sin^2 x = 1