Hi Ahmad
To extract the specific condition "(sin(b) == sin(a)^3)" from the result of the "simplify" function and then substitute it into equation 1 to simplify the expression for "P", you can follow these steps in MATLAB:
- Differentiate equation 1 with respect to a.
- Use the "simplify" function to simplify the differentiated expression.
- Extract the condition "(sin(b) == sin(a)^3)" from the simplified result.
- Substitute this condition into the original equation 1.
- Simplify the result to get the expression for "P" in terms of a only.
Here's how you can do this in MATLAB:
syms a b k l P
% Define the original equation
P = k * l * cos(a) * (1 - (sin(b)/sin(a)))
% Differentiate P with respect to a
dPda = diff(P, a)
% Simplify the differentiated expression
simplified_dPda = simplify(dPda)
% Assuming you have the condition sin(b) == sin(a)^3 from the simplified result
% Substitute this condition into the original equation for P
P_substituted = subs(P, sin(b), sin(a)^3)
% Simplify the substituted expression for P
simplified_P = simplify(P_substituted)
After running this code, "simplified_P" should contain the simplified expression for P after substituting the condition "(sin(b) == sin(a)^3)" into the original equation. If the condition is not automatically extracted from the simplification process, you can manually apply the substitution as shown in the code above.
Hope this helps!
