Question

if sec theta= 25/7 then find the value of tan​

Answer 1

Answer:

sec^2Theta - tan^2theta = 1

(25/7)^2 - tan^2theta = 1

625/49 - tan^2 theta = 1

625/49 - 1 = tan^2 theta

576/49 = tan^2theta

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 \thetatanθ[/tex]

As,

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

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

Using identity,

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

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

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

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

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