Question

33-34 примеры(тригонометрия)

Answer 1

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

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

Answer 2

(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