Question

If sec θ = `25/7`, then find the value of tan θ.

Solution:

1 + tan² θ = `square`

∴ 1 + tan² = `square^2`

∴ tan² θ = `625/49 -  square`

= `(625 - 49)/49`

tan² θ = `576/49`

tan θ = `square`

Answer 1

1 + tan² θ = \[\boxed{sec^2 θ}\]

∴ 1 + tan² = \[\boxed{\left(\frac{25}7\right)^2}\] 

∴ tan² θ = `625/49 -` \[\boxed{1}\]

= `(625 - 49)/49`

tan² θ = `576/49`

tan θ = \[\boxed{\frac{24}7}\]