If $\alpha = 22^\circ 30',$ then $(1 + \cos \alpha )(1 + \cos 3\alpha )$ $(1 + \cos 5\alpha )(1 + \cos 7\alpha )$ equals

  • A

    $1/8$

  • B

    $1/4$

  • C

    $\frac{{1 + \sqrt 2 }}{{2\sqrt 2 }}$

  • D

    $\frac{{\sqrt 2 - 1}}{{\sqrt 2 + 1}}$

Similar Questions

If $\frac{\sin ^4 x}{2}+\frac{\cos ^4 x}{3}=\frac{1}{5},$ then

$(A)$ $\tan ^2 x=\frac{2}{3}$ $(B)$ $\frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{1}{125}$

$(C)$ $\tan ^2 x=\frac{1}{3}$ $(D)$ $\frac{\sin ^8 x}{8}+\frac{\cos ^8 x}{27}=\frac{2}{125}$

  • [IIT 2009]

If $x = a{\cos ^3}\theta ,y = b{\sin ^3}\theta ,$ then

If $\sin \theta + \cos \theta = m$ and $\sec \theta + {\rm{cosec}}\theta = n$, then $n(m + 1)(m - 1) = $

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Prove that $\cos \left(\frac{\pi}{4}-x\right) \cos \left(\frac{\pi}{4}-y\right)-\sin \left(\frac{\pi}{4}-x\right) \sin \left(\frac{\pi}{4}-y\right)=\sin (x+y)$