Упростите выражение 1) cos^2-1 2)(1-sin t) (1+sin t) 3)cos^2t +1 - sin^2t 4) (sin t + cos t)^2/1+2 sin t cos t

Упростим тригонометрические выражения: 

1) cos^2 t - 1 = cos^2 t - (cos^2 t + sin^2 t) = cos ^2 t - cos^2 t  - sin^2 t = -sin^2 t; 

2) (1 - sin t) * (1 + sin t) = 1^2 - sin^2 t = cos^2 t + sin^2 t - sin^2 t = cos^2 t; 

3) cos^2 t + 1 - sin^2 t = cos^2 t + cos^2 t + sin^2 t - sin^2 t = cos^2 t + cos^2 t  = 2 * cos^2 t; 

4) (sin t + cos t)^2/(1 + 2 * sin t * cos t) = (sin t + cos t)^2/(sin^2 t + cos^2 t + 2 * sin t * cos t) = (sin t + cos t)^2/(sin^2 t + 2 * sin t * cos t + cos^2 t) = (sin t + cos t)^2/(sin t + cos t)^2 = 1.