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From your third last step onwards, you are making major mistakes. Firstly,in that step you cancel 2 from 2cos(A) while neglecting the sqrt2 term . After that the cos(A) vanishes ...

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0 fordisplaystylefracsinleft(5pi ight)3anddisplaystyle-fracsqrt32fordisplaystylesinleft(frac5π3 ight) Explanation: displaystylefracsinleft(5pi ight)3=frac03=0 ...
displaystyle-fracsqrt22 Explanation:Trig table of special arcs, unit circle, property of supplementary arcs --> displaystylesinleft(frac5pi4 ight)=sinleft(fracpi4+frac4pi4 ight)=sinleft(fracpi4+pi ight)=-sinleft(fracpi4 ight)=-fracsqrt22
sine, left parenthesis, start fraction, 5, pi, divided by, 4, kết thúc fraction, right parenthesis, equals, sine, left parenthesis, start fraction, pi, divided by, 4, over fraction, plus, start fraction, 4, pi, divided by, 4, end fraction, right parenthesis, equals, sine, left parenthesis, start fraction, pi, divided by, 4, end fraction, plus, pi, right parenthesis, equals, minus, sine, left parenthesis, start fraction, pi, divided by, 4, over fraction, right parenthesis, equals, minus, start fraction, square root of, 2, end square root, divided by, 2, end fraction" role="text" class="MathExpression_mathExpression__22QI1 ">
displaystylesinleft(frac5pi6 ight)=frac12 Explanation:It is an angle at the second quadrant with reference angle displaystyle=fracpi6 . displaystylesinleft(frac5pi6 ight)=sinleft(fracpi6 ight)=frac12 ...

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Actually it is very easy lớn find thatdisplaystyleleftlbracesinleft(frac5pi12 ight)=fracsqrt6+sqrt24 ight. .Explanation:You use the formula for ...
displaystyle-1 Explanation:Use displaystylesinleft(-x ight)=-sinxquad extandquadsinleft(2pi+x ight)=sinx Here,displaystylesinleft(-frac5pi2 ight)=-sinleft(frac5pi2 ight)=-sinleft(2pi+fracpi2 ight)=-sinleft(fracpi2 ight)=-1 ...
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left< eginarray l l 2 & 3 \ 5 & 4 endarray ight> left< eginarray l l l 2 & 0 & 3 \ -1 & 1 & 5 endarray ight>
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