tg^2(a)+sin^2(a)-1/(cos^2(a)) (cos(3 a)+cos(a))/(2 cos(a))+2 sin^2(a)

Question

tg^2(a)+sin^2(a)-1/(cos^2(a))

(cos(3 a)+cos(a))/(2 cos(a))+2 sin^2(a)

Answer 1

1)tg^2(a)+sin^2(a)-1/(cos^2(a))=sin^2(a)/cos^2(a)+sin^2(a)-1/cos^2(a)=(sin^2(a) - sin^2(a)-cos^2(a)+sin^2(a)*cos^2(a))/cos^2(a)=(cos^2(a)(sin^2(a)-1))/cos^2(a)= sin^2(a)-1= sin^2(a)- sin^2(a)-cos^2(a)= -cos^2(a) 

2)(cos(3 a)+cos(a))/(2 cos(a))+2 sin^2(a)=((4cos^3(a)-3cos(a)+cos(a))/2cos(a))+2sin^2(a)= ((4cos^3(a)-2cos(a))/2cos(a))+2sin^2(a)=2cos(a)*(2cos^2(a)-1)/2cos(a)+2sin^(a)=2cos^2(a)-cos^2(a)-sin^2(a)+2sin^2(a)=cos^2(a)+sin^2(a).