if secA-tanA =10 than sinA =?,cosA =?,secA =?

Answer 1

use sec²A=1+tan²A
and let t=tan(A)

sec(A)-tan(A)=10
√(1+t^2)-t=10
√(1+t^2)=(t+10)²
1=20t+100
t=-99/20
A=atan(-99/20)=-78.5788 (approx.)

sec(A)=1/√(1+t^2)=101/20
cos(A)=1/sec(A)=20/101
sin(A)=-sqrt(1-(20/101)^2)=99/101
(note: A is in Q4, so sin(A)<0)