Question

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

1 + tan²θ = sec²θ

Answer 1

Given: θ = 30°

To prove: 1 + tan²θ = sec²θ

Proof:

L.H.S. = 1 + tan²θ

= 1 + tan²30°

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

= `1 + 1/3`

L.H.S. = `4/3`  ...(i)

Now, R.H.S. = sec²θ

= sec²30°

= `(2/sqrt3)^2`

R.H.S. = `4/3` ...(ii)

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

∴ 1 + tan²θ = sec²θ