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4 cos 2 (x) + 7sin (x) – 7 = 0 (1) Using the identity sin 2 (x) + cos 2 (x) = 1, rearrange to give; cos 2 (x) = 1 - sin 2 (x) (2) Sub (2) into (1) ... Giving; 4 ( 1 - sin 2 (x) ) + 7sin (x) - 7 = 0 Expand br...

To find the factors of x 3 -7x-6, a method called equating coefficients can be used. Firstly, set the equation to zero and find a suitable number which satisfies the equation, in this case x=-1 satisfies the...

y=a^x take natural logs (also written as ln or log base e) of both sides lny=lna^x by logarithms rules lna^x=xlna lny=xlna Now differentiate implicitly 1/y = (dx/dy)lna Note here lna is just a constant, then...

There are a number of integrals that we can evaluate directly, called elementary functions:integral[ x dx ] = x 2 /2 + Cintegral[cos( x ) dx ] = sin( x ) + C However, most integrals cannot be solved so direc...

Problems of this style are solved using the chain rule. To begin, define the quantity inside the brackets as u u = 6x-1 such that y = u^7 It is now useful to write the chain rule. We can see dy/dx = du/dx x ...