Question

Simplify:

cot (90° − θ) x `sin (90° − θ)/cos (90° − θ)`

Answer 1

cot (90° − θ) = tan θ, sin (90° − θ) = cos θ, cos (90° − θ) = sin θ.

Given expression becomes:

`cot (90° −  θ) xx sin (90° − θ)/cos(90° −  θ) = tan θ xx cosθ/sinθ`

Since `cosθ/sinθ` = cot θ,    ...[we get]

tan θ × cot θ = 1