Question

Taking θ = 30° to verify the following trigonometric identity:

1 + cot²θ = cosec²θ

Answer 1

Given: θ = 30°

To prove: 1 + cot²θ = cosec²θ

Proof:

L.H.S. = 1 + cot²θ

= 1 + cot²30°

= `1 + (sqrt3)^2`

= 1 + 3

= 4  ...(i)

Now, R.H.S. = cosec²θ

= cosec²30°

= `(2/1)^2`

= 4  ...(ii)

∴ L.H.S. = R.H.S.  ...[From equations (i) and (ii)]

∴ 1 + cot²θ = cosec²θ