Question

$\sqrt{(1-{\cos }^2\theta ){\sec }^2\theta }=\tan \theta$.Is it true or false?

• A. True
• B. False
• C. Ambiguous
• D. Data insufficient
  

Answer 1

The correct option is A True

$\sqrt{(1-{\cos }^2\theta ){\sec }^2\theta }$

$=\sqrt{si{n}^2\theta \times {\sec }^2\theta }$

$=\sin \theta \times \sec \theta$

$=\frac{\sin \theta }{\cos \theta }$

$=\tan \theta$

Hence True.