The value of the expression

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Question

$\frac{{{{(\sin 36 + \cos 36)}^2} - 2{{\sin }^2}{{27}^\circ }}}{{2\sin {{54}^\circ }}}$

$ = \frac{{\cos {{54}^\circ } + \cos {{18}^\circ }}}{{2\sin

Vedclass · Accepted Answer

$\cos {9^o}$

Vedclass · Answer

$\frac{{{{(\sin 36 + \cos 36)}^2} - 2{{\sin }^2}{{27}^\circ }}}{{2\sin {{54}^\circ }}}$

$ = \frac{{\cos {{54}^\circ } + \cos {{18}^\circ }}}{{2\sin {{54}^\circ }}} = \frac{{2\cos {{36}^\circ }\cos {{18}^\circ }}}{{2\cos {{36}^\circ }}}$

${=\cos 18^{\circ}<\cos 9^{\circ}}$

The value of the expression

$\frac{{\left (sin 36^o + cos 36^o - \sqrt 2 sin 27^o)( {\sin {{36}^0} + \cos {{36}^0} - \sqrt 2 \sin {{27}^0}} \right)}}{{2\sin {{54}^0}}}$ is less than

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