sec θ. cot θ = cosec θ write true or false.

True

Reason:

sec θ. cot θ = cosec θ

L.H.S. = sec θ. cot θ

$= \dfrac{1}{\text{cos θ}} \times \dfrac{\text{cos θ}}{\text{sin θ}}\\[1em] = \dfrac{1}{\cancel{\text{cos θ}}} \times \dfrac{\cancel{\text{cos θ}}}{\text{sin θ}}\\[1em] = \dfrac{1}{\text{sin θ}}\\[1em] = \text{cosec θ}$

R.H.S. = cosec θ

∴ L.H.S. = R.H.S.