Asked by Britt
Use identities to simplify each expression.
1) (sin2t) (cos5t) + (cos2t) (sin5t)
2) {1/(sec x - 1)} - {1/(sec x +1)} = 2 cot^2 x
1) (sin2t) (cos5t) + (cos2t) (sin5t)
2) {1/(sec x - 1)} - {1/(sec x +1)} = 2 cot^2 x
Answers
Damon
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(1-cos x)]/(1-cos^2 x)
[ cos x + cos^2x - cos x +cos^2 x]/sin^2x
2 cos^2 x/sin^2 x
2 cot^2 x
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(1-cos x)]/(1-cos^2 x)
[ cos x + cos^2x - cos x +cos^2 x]/sin^2x
2 cos^2 x/sin^2 x
2 cot^2 x