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To find inverse functions we swap the variables of the function we are taking the inverse of. let y=1+2sin(3x)so now, x=1+2sin(3y)Aiming to make y the subject, x-1= 2sin(3y)Therefore, (x-1)/2=sin(3y), ...

By product rule:u = 4sin(x) v = cos(3x)du/dx = 4cos(x) dv/dx = -3sin(3x)dy/dx = u (dv/dx) + v (du/dx)dy/dx = 4sin(x) * -3sin(3x) + cos(3x) * 4cos(x)dy/dx = -12sin(x)sin(3x) + 4cos(x)cos(3x)Evaluate at x =...

We can explain this by taking a simple power equation such as 2³ = 8 and setting each number as an unknown variable. For instance 2³ = x is solved by cubing 2, x³ = 8 is s...

1. you cannot integrate cos^2(4x) without making substitutions first. Use the cos^2(x) + sin^2(x) = 1 identity with the cos(2x)=cos^2(x)-sin^2(x), rearrange to get the identity cos(2x) = 2cos^2(x) - 1,...

Using simple trig identities, we know tan^2(A) + 1 = sec^2(A).Substituting for sec^2(A) into our equation, we get: tan^2(A) + 1 = 3 - tan(A).Moving this over to one side, we get the quadratic in terms of ...