33-34 примеры(тригонометрия). Created by shynar025. algebra-ru

33-34 примеры(тригонометрия)...

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$33)\; \; (sina+ \frac{1}{sina})^2+(cosa + \frac{1}{cosa})^2-tg^2a-ctg^2a=\\\\= sin^2a+2+ \frac{1}{sin^2a}+cos^2a+2+ \frac{1}{cos^2a} -tg^2a-ctg^2a=\\\\=(sin^2a+cos^2a)+4+(1+ctg^2a)+(1+tg^2a)-tg^2a-ctg^2a=\\\\=1+4+1+1=7$

$34)\; \; sin( \frac{\pi }{4}-a)\cdot sin(\frac{\pi}{4}+a)-cos(\frac{\pi }{4}+a)\cdot cos(\frac{\pi }{4}-a)=\\\\=-cos( (\frac{\pi }{4}+a)+(\frac{\pi }{4}-a))=-cos\frac{\pi }{2} =0$

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sedinalana (sina+1/sina)²+(cosa+1/cosa)²-tg²a-ctg²a=
=sin²a+2+1/sin²a+cos²a+2+1/cos²a-tg²a-ctg²a=
=1/sin²a+5+1/cos²a-tg²a-ctg²a=(1/sin²a-1)+(1/cos²a-1)+7-tg²a-ctg²a=
=tg²a+ctg²a+7-tg²a-ctg²a=7

sin(π/4-a)sin(π/4+a)-cos(π/4-a)cos(π/4+a)=
=-(cos(π/4-a)cos(π/4+a)-sin(π/4-a)sin(π/4+a))=-cos(π/4-a+π/4+a)=-cosπ/2=0

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