Question

Need some urgent trig help please!!

Use trigonometric expressions to build an equivalent trigonometric identity with the given expression: (1-cos^2(x))(1+cos^2(x))/(cos^2(x)

Answer 1

Alright, so..
(1-cos^2(x)) = sin2x

So the given expression can be written as sin2x(1+cos2x)/cos2x which can combine the first part of the numerator & the denominator to become tan2x, so we now have

tan2x(1+cos2x) = tan2x + sin2x

since tan2x = sin2x / cos2x & marvelous cancellation occurs when distribution is applied.