Question

If sec theta =25/7 then find tan theta

Answer 1

Sec theta =25/7

Cos theta =7/25

By Pythagoras theorem

Tan theta =24/7

Answer 2

Answer:

$\text{The value of }\tan\theta \text{ is }\frac{24}{7}$  

Step-by-step explanation:

Given $\sec \theta=\frac{25}{7}$

we have to find the value of $\tan \theta$

As, $\sec \theta=\frac{25}{7}$

$\cos \theta=\frac{1}{\sec \theta}=\frac{1}{\frac{25}{7}}=\frac{7}{25}$

Using identity,

$\sin^2\theta+\cos^2\theta=1$

$\sin^2\theta=1-\cos^2\theta$

$sin\theta=\sqrt{1-\frac{25}{625}}=\sqrt{\frac{576}{625}}=\frac{24}{25}$

$\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{\frac{24}{25}}{\frac{7}{25}}=\frac{24}{7}$

$\text{The value of }\tan\theta \text{ is }\frac{24}{7}$