Question

1.(1+tg²a)cos²а;   2).tga + tgß       3).cos²a– ctg²a

                           —————;       ——————.

                            ctga + ctgß        sin²a- tg²a

2 жане 3 есеп болшек егер де тусинбесениздер аракашыктыгы алыстап кетти.

Answer 1

(1+tg^2a)*cos^2а=1
(tga+tgß)/(ctga+ctgß)=tga*tgb
(cos^2a–ctg^2a)/(sin^2a-tg^2a)=-ctg^6a

Comments

(1+tg^2a)*cos^2а=(1+y^2/x^2)*x^2/R^2=x^2/R^2+y^2/R^2=x^2+y^2=1

(tga+tgß)/(ctga+ctgß)=(y/x+y1/x1)/(x/y+x1/y1)=((x1*y+x*y1)/(x*x1))/((x*y1+x1*y)/(y*y1))=(y*y1)/(x*x1)=tga*tgb

(cos^2a–ctg^2a)/(sin^2a-tg^2a)=((x^2/R^2-x^2/y^2)/(y^2/R^2-y^2/x^2))=((y^2*x^2-R^2*x^2)/(R^2*y^2))/((y^2*x^2-R^2*y^2)/(R^2*x^2))=(x^4*(y^2-R^2))/(y^4(x^2-R^2))=(x^4*-x^2)/(y^4*-y^2)=(-x^6/(-y^6))=(x^6/y^6)=ctg^6a

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(1+tg^2a)*cos^2а=(1+y^2/x^2)*x^2/R^2=x^2/R^2+y^2/R^2=x^2/R^2+y^2/R^2=R^2/R^2=1