Question

prove that sin theta minus cos theta + 1 upon sin theta + cos theta minus 1 is equal to one upon sec theta minus tan theta​

Answer 1

Hope this helps you out!

Answer 2

PROVED

Step-by-step explanation:

to prove :

$\frac{\sin\theta -\cos\theta+1}{\sin\theta +\cos\theta-1}= \frac{1}{\sec\theta-\tan\theta}$

proof :

$\frac{\sin\theta -\cos\theta+1}{\sin\theta +\cos\theta-1}= \frac{1}{\sec\theta-\tan\theta}\\\\\frac{\frac{\sin\theta}{\cos\theta}- \frac{\cos\theta}{\cos\theta}+ \frac{1}{\cos\theta}}{\frac{\sin\theta}{\cos\theta}+ \frac{\cos\theta}{\cos\theta}- \frac{1}{\cos\theta}}\\\\\frac{\tan\theta-1+\sec\theta}{\tan\theta+1-\sec\theta}= \frac{\tan\theta+\sec\theta-1}{\tan\theta-\sec\theta+1}\\\\\frac{\tan\theta+\sec\theta-1}{\tan\theta-\sec\theta+ ((\sec\theta+\tan\theta)(\sec\theta-\tan\theta))}$

$\frac{\tan\theta+\sec\theta-1}{-(\sec\theta-\tan\theta)+(\sec\theta+\tan\theta)(\sec\theta-\tan\theta)}\\\\\frac{\tan\theta+\sec\theta-1}{(\sec\theta-\tan\theta)(1+\sec\theta+\tan\theta)}\\\\\frac{1}{\sec\theta-\tan\theta}$

hence , proved

#Learn more :

https://brainly.com/question/9108698