If cos A = 7/25, find the value of tan A + cot A.

Question

If cos A = \(\frac{7}{25}\), find the value of tan A + cot A.   

Answer 1

Given: cos A = \(\frac{7}{25}\)

To find: tan A + cot A 

∵ sin² ​​A + cos²A = 1 

⇒ sin²A = 1 – cos²A

⇒ sin A = \(\sqrt{1 – cos^2A}\)

= \(\sqrt{1-\Big(\frac{7}{25}\big)^2}\)  = \(\sqrt{1-\frac{49}{625}}\) 

= \(\sqrt{\frac{625-49}{625}}\) = \(\sqrt{\frac{576}{625}}\) = \(\frac{24}{25}\) 

Now, as tanA = \(\frac{sinA}{cosA}\) = \(\frac{24/25}{7/25}\)  = \(\frac{24}{7}\) 

And cotA = \(\frac{1}{tanA}\) = \(\frac{7}{24}\) 

⇒ tanA + cotA = \(\frac{24}{7}\) + \(\frac{7}{24}\) =  \(\frac{576+49}{168}\) = \(\frac{625}{168}\)