is either of these true - sin(theta)/cot(theta)-sec(theta) = -cos(theta) and cos(theta)+tan(theta)xsin(theta)= sec(theta)

Let's see...working with the LHS, we have

- sin(theta)/cot(theta)-sec(theta) = -cos(theta)

-sin(x) / [cos(x)/sin(x)] - 1/cos(x)

-sin^2(x) / cos (x) - 1/cos(x)

- [ 1 + sin^2(x) ] / cos(x) =  -cos(x)   ???.....nope....no way this is true....!!!

And

cos(theta)+tan(theta)xsin(theta)= sec(theta)

Working on the LHS, we have....

cos(x) + [ sin^2(x) / cos(x) ]

[cos^2(x) + sin^2(x) ] / cos(x) =

1 / cos(x)  =  sec(x).......  and this one is true....!!!!