Question

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

1 + cot² θ = cosec² θ

Answer 1

Given: θ = 30°

To prove: 1 + cot² θ = cosec² θ

Proof:

L.H.S. = 1 + cot² θ

= 1 + cot² 30°

= `1 + (sqrt3)^2`

= 1 + 3

= 4  ...(i)

Now, R.H.S. = cosec² θ

= cosec² 30°

= `(2/1)^2`

= 4    ...(ii)

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

∴ 1 + cot² θ = cosec² θ