Question

express tan theta in terms of sec theta

Answer 1

$\sec ^{2} (x ) - \tan^{2} (x) = 1 \\ or. \: \tan^{2} (x) = 1 - \sec^{2} (x) \\ or. \: \tan(x) = \sqrt{1 - { \sec }^{2}(x) } .$
Put theta in place of x.
Hope this would help u out.

Answer 2

Answer:

The required expression is $\tan\theta=\sqrt{1-\sec^2\theta}$

Step-by-step explanation:

To express : $\tan\theta$ in terms of $\sec\theta$ ?

Solution :

Using trigonometric identities,

$\sec^2\theta-\tan^2\theta=1$

Arrange, $\tan\theta$ in terms of $\sec\theta$

$\tan^2\theta=1-\sec^2\theta$

Taking root both side,

$\sqrt{\tan^2\theta}=\sqrt{1-\sec^2\theta}$

$\tan\theta=\sqrt{1-\sec^2\theta}$

Therefore, The required expression is $\tan\theta=\sqrt{1-\sec^2\theta}$