Use identities to simplify each expression.

Question

1) (sin2t) (cos5t) + (cos2t) (sin5t)
2) {1/(sec x - 1)} - {1/(sec x +1)} = 2 cot^2 x

Answer 1

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