Simplifying Trigonometric Expression

Question

Simplify the following trigonometric expression so that the final answer contains ONLY ONE trigonometric function, and contains NO fractions.

(sin^2 θ)(cot^2 θ)(sec^2 θ)

Answer 1

= (sinTcotTsecT)^2

= (sinT(cosT/sinT)(1/cosT)^2

= (cosT/coT)^2

=1^2

= 1

but that's not a trig function. you wanted 1 trig function

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

= sin^2(x) +1-sin^2(x)) is 1 and only 1 trig function

or just sinx +1 -sinx

or 1 + and - any trig function

Answer 2

Answer 3

sin²θ cot²θ sec²θ = sin²θ (cos²θ / sin²θ)(1 / cos²θ) = (sin²θ cos²θ) / (sin²θ cos²θ) = 1