Question

solve 2sec^2x-tan^4x=3, find x in terms of pi

Answer 1

1+tan^2(x)=sec^2(x) (trig identity).

2(1+tan^2(x))-tan^4(x)=3; 2+2tan^2(x)-tan^4(x)=3; tan^4(x)-2tan^2(x)+1=0;

(tan^2(x)-1)^2=0, tan^2(x)-1=0; tan^2(x)=1; tan(x)=+1, so x=(pi)/4 or -(pi)/4. General solution is (2n-1)(pi)/4 where n is an integer.