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From the following identity, cos(a-b) = cosacosb+ sinasinb, we find that 4sinx+3cosx = R(cosxcosa+sinxsina). We now equate the coefficients: 3 = Rcosa and 4=Rsina. Using basic trigonometry, we can make th...

Firstly square both sides. This way, we now know that both sides have to be positive

(3x+1)^2 = 1

(3x+1)(3x+1) = 1

Expand the quadratic...

9x^2 + 12x + 4 = 1

9x^2 + 12x ...

So we are meant to rearrange the given equation in a way that it looks like: (x+p)^2 + q This should look familiar. It is obtained by completing the square. Which will be the method I will describe below:...

The conditional is a useful tense, used to express things that could/would/should happen. They are commonly followed by an 'if', for example:

I would go to the supermarket if I had some money - J'i...

If the birthrate in a country is too high, there will be many children, which will lead to a population explosion and a very rapid population growth - which may not be sustainable in terms of space or res...