How to substitute value in equation already have

P=k*l*cos(a)*(1-(sin(b)/sin(a))) -----------1

sin(a)=sin(b)^3 ---------2

What i have done is differentiated the eq-1 with respect to a and got the eq-2 in form of long variable like ~in(a/pi, 'integer') & (sin(b) == sin(a)^3 | k == 0 | l == 0)

I have used the diff function and then simplify that equation in MATLAB itself and getting this ~in(a/pi, 'integer') & (sin(b) == sin(a)^3 | k == 0 | l == 0

my QUESTION is that

1. how I could able to take the only (sin(b) == sin(a)^3 from the simply result
2. And after taking it from the simplify function substitute in the equation 1 to get something like P= k*l*cos(a)^3 after everything

thank you

Answer 1

[Vaibhav]

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:

1. Differentiate equation 1 with respect to a.
2. Use the "simplify" function to simplify the differentiated expression.
3. Extract the condition "(sin(b) == sin(a)^3)" from the simplified result.
4. Substitute this condition into the original equation 1.
5. 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)))

P = 

% Differentiate P with respect to a
dPda = diff(P, a)

dPda = 

% Simplify the differentiated expression
simplified_dPda = simplify(dPda)

simplified_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)

P_substituted = 

% Simplify the substituted expression for P
simplified_P = simplify(P_substituted)

simplified_P = 

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!