trigonometry
posted by Britt .
1) (sin2t) (cos5t) + (cos2t) (sin5t)
2) {1/(sec x  1)}  {1/(sec x +1)} = 2 cot^2 x

sin a cos b + cos a sin b = sin (a+b)
so sin (7t)
1/(1/cos x 1)  1/(cos x +1)
cos x/(1  cos x)  cos x/(1+cos x)
[cos x(1+cos x)  cos x(1cos x)]/(1cos^2 x)
[ cos x + cos^2x  cos x +cos^2 x]/sin^2x
2 cos^2 x/sin^2 x
2 cot^2 x