Question

Verify the following equalities:

1 + tan² 30° = sec² 30°

Answer 1

tan 30° = `1/sqrt(3)`, sec 30° = `2/sqrt(3)`

L.H.S = 1 + tan² 30°

= `1 + (1/sqrt(3))^2`

= `1 + (1/3)`

= `((3 + 1)/3)`

= `4/3`

R.H.S = sec² 30°

= `(2/sqrt(3))^2`

= `4/3`

∴ L.H.S = R.H.S

Hence it is proved.