Question

second derivative of sin 2a csc a + cos a

Answer 1

Easy trick for this question:

The expression sin 2a csc a can be simplified to (2 sin a cos a)(1/sin a) = 2 cos a

I used the double-angle formula from trig that states sin (2a) = 2 sin a cos a
and the fact that csc a = 1 /sin a

So the original expression that you want to find the second derivative of, is really 2 cos a + cos a = 3 cos a

The first derivative of 3 cos a -s -3 sin a.
And the derivative of -3 sin a is -3 cos a.

So, the second derivative is -3 cos a.