Question

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

1 + tan² θ = sec² θ

Answer 1

Given: θ = 30°

To prove: 1 + tan² θ = sec² θ

Proof:

L.H.S. = 1 + tan² θ

= 1 + tan² 30°

= `1 + (1/sqrt3)^2`

= `1 + 1/3`

= `4/3`  ...(i)

Now, R.H.S. = sec²θ

= sec²30°

= `(2/sqrt3)^2`

= `4/3` ...(ii)

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

∴ 1 + tan² θ = sec² θ

Hence proved.