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To start, we use the inverse trigonometric formulae to convert the 'cot' function into a 'tan' function: cot(2x)=1/(tan(2x))=3 Inverting this gives: tan(2x)=1/3 2x=arctan(1/3)=18.43°or (180+18.43)° Therfo...

Expanding and simplifying the right hand side: x²=4(x-3)(x-3)=4(x²-6x+9)=4x²-24x+36 Deducting 'x²' from both sides: 0=3x²-24x+36 Dividing by 3 and fa...

x^2+12x-45

x^2+15x-3x-45 (15x - 3x= 12x and 15 x -3=-45)

x(x+15)-3(x+15)

(x-3)(x+15) 

The expression is of the form ax^2 + bx + c. Here, a = 1 and this makes it easier for us. We can also see that b = 5 and c = 6. In general, we have to find two numbers that multiply to get c and add to ge...

To answer this question you need to group the different terms to form the shortest equation possible. It is easiest to treat the x terms and the y term as seperate, so you have:

2x - x      and    ...