How do you simplify tan t * cot t - sin^2 ttantcottsin2t?

2 Answers
Sep 1, 2015

cos^2tcos2t

Explanation:

tan tcot t= tan tx (1/tan t)=1tantcott=tantx(1tant)=1
1-sin^2t=(sin^2 t+cos^2 t)-sin^2 t=cos^2t1sin2t=(sin2t+cos2t)sin2t=cos2t

Sep 1, 2015

This problem requires some trigonometric identities,here,
1) cotx=1/tanx
2)sin^2xsin2x+cos^2xcos2x=1 or cos^2xcos2x=1-sin^2xsin2x

Explanation:

1) tan t*cot t -sin^2tsin2t* = tan t 1/tan t-sin^2tsin2t........(putting identity .1)
= 1-sin^2tsin2t................(putting identity .2)
= cos^2tcos2t
....................................................................................................................
I hope this helps :)