Question

If `tan θ = 7/24`, then to find value of cos θ complete the activity given below.

Activity:

sec²θ = 1 + `square`   ...[Fundamental tri. identity]

sec²θ = 1 + `square^2`

sec²θ = 1 + `square/576`

sec²θ = `square/576`

sec θ = `square` 

cos θ = `square`   ...`[cos theta = 1/sectheta]`

Answer 1

\[\text{sec}^2θ = 1 + \boxed{\text{tan}^2θ}\]   ...[Fundamental tri. identity]

∴ \[\text{sec}^2θ = 1 + \boxed{\frac{7}{24}}^2\]

∴ \[\text{sec}^2θ = 1 + \frac{\boxed{49}}{576}\]

∴ sec²θ = `(576 + 49)/576`

∴ \[\text{sec}^2θ = \frac{\boxed{625}}{576}\]

∴ \[\text{sec} \phantom{.}θ = \boxed{\frac{25}{24}}\]

∴ \[\text{cos} \phantom{.}θ = \boxed{\frac{24}{25}}\]   ...`[cos theta = 1/sectheta]`