Question

If \[\tan A = \frac{5}{12}\] \[\tan A = \frac{5}{12}\]  find the value of (sin A + cos A) sec A. 

Answer 1

Given:  tan` A=5/12` 

`"Perpendicular"/"Base"=5/12` 

`"Perpendicular"=5` 

`Base=12` 

`"Hypotenuse"= sqrt(("Perpendicular")^2+("Base")^2)`

We know that: ` tan A="Perpendicular"/"Base"` 

`"Hypotenuse"=sqrt((5)^2+(12)^2)`  

`"Hypotenuse"=sqrt169` 

`"Hypotenuse"=13` 

Now we find, `(sin A+cos A) SecA`

⇒ `(Sin A+Cos A)Sec A=(5/13+12/13)xx13/12` 

⇒ `(sin A+cos A)sec A=17/13xx13/12` 

⇒ `(sin A+cos A) sec A=17/12`

Hence the value of` (sin A+ cos A)sec A  "is" 17/12`