Question

Which of the following is an identity? Also, please include an explanation.

sinθcotθsecθ = 0, sinθcotθsecθ = 1, sinθcotθsecθ = cot2θ, or sinθcotθsecθ = tan2θ?

Answer 1

`cot\theta= ( cos \theta)/( sin \theta ) \\ sec\theta = (1)/( cos \theta ) \\ \\ \\ sin \theta cot\theta sec\theta \\ = sin \theta \cdot ( cos \theta)/( sin \theta ) \cdot (1)/( cos \theta ) \\ = ( sin \theta)/( sin \theta ) =1 \\`


sinθcotθsecθ = 1