Question

If \[\cos A = \frac{7}{25}\]  find the value of tan A + cot A. 

Answer 1

Given:  `cos A=7/25` 

We know that, 

`sin^2 A+cos^2 A=1` 

⇒` sin^2 A+(7/25)^2=1` 

⇒` sin^2 A+49/625=1` 

⇒` sin^2 A1-49/625` 

⇒ `sin^2A=576/625` 

⇒ `sin A=24/25` 

Therefore, 

`tan A+cot A= sin A/cos A+cos A/sin A` 

=` (24/25)/(7/25)+1=(7/25)/(24/25)` 

= `24/7+7/24` 

=`((24)^2+(7)^2)/168`  

=`(576+49)/168` 

=`625/168`