Let $0 < x < \frac{\pi }{4}.$ Then $\sec 2x - \tan 2x = $

  • [IIT 1994]
  • A

    $\tan \left( {x - \frac{\pi }{4}} \right)$

  • B

    $\tan \left( {\frac{\pi }{4} - x} \right)$

  • C

    $\tan \left( {x + \frac{\pi }{4}} \right)$

  • D

    ${\tan ^2}\left( {x + \frac{\pi }{4}} \right)$

Similar Questions

If $\tan \theta = \frac{{\sin \alpha - \cos \alpha }}{{\sin \alpha + \cos \alpha }},$ then $\sin \alpha + \cos \alpha $ and $\sin \alpha - \cos \alpha $ must be equal to

$\left( {1 + \cos \frac{\pi }{8}} \right)\,\left( {1 + \cos \frac{{3\pi }}{8}} \right)\,\left( {1 + \cos \frac{{5\pi }}{8}} \right)\,\left( {1 + \cos \frac{{7\pi }}{8}} \right) = $

  • [IIT 1984]

$\frac{{\sin 3A - \cos \left( {\frac{\pi }{2} - A} \right)}}{{\cos A + \cos (\pi + 3A)}} = $

Prove that $\cot x \cot 2 x-\cot 2 x \cot 3 x-\cot 3 x \cot x=1$

If $\alpha $ and $\beta $ are solutions of $sin^2\,x + a\, sin\, x + b = 0$ as well that of $cos^2\,x + c\, cos\, x + d = 0$ , then $sin\,(\alpha + \beta )$ is equal to