Question

State whether the given statement is true or false

$\sqrt{\frac{1+\sin \theta }{1-\sin \theta }}=\sec \theta -\tan \theta ,-\frac{\pi }{2}<\theta <\frac{\pi }{2}$.

• A. True
• B. False

Answer 1

The correct option is B False

Given, $\sqrt{\frac{(1+sin\theta )}{(1-sin\theta )}}=(sec\theta -tan\theta )$
$LHS=\sqrt{\frac{(1+sin\theta )}{(1-sin\theta )}}$
$=\sqrt{\frac{(1+sin\theta )\ast (1+sin\theta )}{(1-sin\theta )\ast (1+sin\theta )}}$
$=\sqrt{\frac{(1+sin\theta {)}^2}{(1-si{n}^2\theta )}}$
$=\sqrt{\frac{(1+sin\theta {)}^2}{\left(co{s}^2\theta \right)}}$
$=\frac{(1+sin\theta )}{\left(cos\theta \right)}$
$=(sec\theta +tan\theta )\ne RHS$