Вычислите. cos105-sin 195+sin(-135)-cos135 tg18*tg288+sin32*sin148-sin302*sin122 . Created by масяня3009. algebra-ru

Вычислите. cos105-sin 195+sin(-135)-cos135 tg18*tg288+sin32*sin148-sin302*sin122...

масяня3009 @масяня3009

July 2022 1 13 Report

Вычислите.

cos105-sin 195+sin(-135)-cos135

tg18*tg288+sin32*sin148-sin302*sin122

Answers & Comments

Artem112

Verified answer

$\cos105^\circ-\sin 195^\circ+\sin(-135^\circ)-\cos135^\circ=$
$=\cos(90^\circ+15^\circ)-\sin (180^\circ+15^\circ)+\sin(-180^\circ+45^\circ)-\cos(180^\circ-45^\circ)=$
$=-\sin15^\circ-(-\sin 15^\circ)-\sin45^\circ-(-\cos45^\circ)=
\\\
=-\sin15^\circ+\sin 15^\circ-\sin45^\circ+\cos45^\circ=- \dfrac{ \sqrt{2} }{2} + \dfrac{ \sqrt{2} }{2} =0$

$\mathrm{tg}18^\circ\mathrm{tg}288^\circ+\sin32^\circ\sin148^\circ-\sin302^\circ\sin122^\circ=
\\\
=\mathrm{tg}18^\circ\mathrm{tg}(270^\circ+18^\circ)+\sin32^\circ\sin(180^\circ-32^\circ)-
\\\
-\sin(360^\circ-58^\circ)\sin(180^\circ-58^\circ)=
\\\
=\mathrm{tg}18^\circ(-\mathrm{ctg}18^\circ)+\sin32^\circ\sin32^\circ
-(-\sin58^\circ)\sin58^\circ=$
$=-\mathrm{tg}18^\circ\mathrm{ctg}18^\circ+\sin^232^\circ+\sin^258^\circ=
\\\
=-1+\sin^232^\circ+\sin^2(90^\circ-32^\circ)=
\\\
=-1+\sin^232^\circ+\cos^232^\circ=-1+1=0$

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