Question

(Tan^2x-sin^2x)cotan^4x

Sederhanakan trigonometri ini

Answer 1

(tan^2 x - sin^2 x).cot^4 x
= (sin^2 x/cos^2 x - sin^2 x).cos^4 x/sin^4 x
= ((sin^2 x - sin^2 x cos^2 x)/cos^2 x) . cos^4 x/sin^4 x
= (sin^2 x - sin^2 x cos^2 x) . cos^2 x/sin^4 x
= sin^2 x . (1 - cos^2 x) . cos^2 x/sin^4 x
= (1 - cos^2 x) . cos^2 x/sin^2 x
= sin^2 x . cos^2 x/sin^2 x
= cos^2 x