Why is my symbolic trig expression is not fully simplifying?

When I run the following,

syms x

y = sqrt(1-sin(x)^2)

y = simplify(y)

the "simplify" function is not working as expected, i.e. I am not getting an output of "cos(x)" or "abs(cos(x))". Instead, "y" is simply left unchanged.

Answer 1

[MathWorks Support Team]

By default, "simplify" only performs one simplification step, and that is why some expressions, like the one in the question, are not fully reduced. However, you can get a better answer by forcing "simplify" to perform more steps:

<https://www.mathworks.com/help/symbolic/simplify.html?s_tid=doc_ta#btrv5w6-1>

In your example, I began getting the right answer after raising "Steps" to 15:

syms x

y = sqrt(1-sin(x)^2)

y = simplify(y,'Steps',15);

Now the output of "simplify" is "abs(cos(x))" as expected.