Question

If sec θ = `25/7`, complete the following activity to find the value of tan θ.

Activity:

We have, 1 + tan²θ = sec²θ

∴ 1 + tan²θ = `square`

∴ tan²θ = `625/49 - square`

∴ tan²θ = `(625 - 49)/(49)`

∴ tan²θ = `square/49`

∴ tan²θ = `square`

Answer 1

We have, 1 + tan²θ = sec²θ

∴ 1 + tan²θ = \[\boxed{\left(\frac{25}7\right)^2}\] 

∴ tan²θ = `625/49 -` \[\boxed{1}\]

∴ tan²θ = `(625 - 49)/49`

∴ tan²θ = \[\frac{\boxed{576}}{49}\]

∴ tan²θ = \[\boxed{\frac{24}7}\]