Question

Is LHS=RHS?
$\frac{\sin \theta +\cos \theta }{\sin \theta -\cos \theta }+\frac{\sin \theta -\cos \theta }{\sin \theta +\cos \theta }=\frac{2}{{\sin }^2\theta -{\cos }^2\theta }=\frac{2{\sec }^2\theta }{{\tan }^2\theta -1}$

• A. Yes
• B. No
• C. Ambiguos
• D. Can't say

Answer 1

The correct option is A Yes

Simplifying, we get
$\frac{(sin\theta +cos\theta {)}^2+(sin\theta -cos\theta {)}^2}{si{n}^2\theta -co{s}^2\theta }$
$=\frac{2}{si{n}^2\theta -co{s}^2\theta }$
$=\frac{2}{co{s}^2\theta (ta{n}^2\theta -1)}$
$=\frac{2se{c}^2\theta }{ta{n}^2\theta -1}$