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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...

First, we have to know that if 2 lines are perpendicular, the product of their gradients is -1.

Next, we have to express the 2 equations in similar ways by rearranging them and making y the common ...

To solve this equation for x, we need to get x on its own. To do this, we first need to multiply through by the denominators of the fractions, as none of them contain an x term. Multiplying through by 8 f...

With differentiation and integration, we can take each term separately. In general, to difference a term involving x's with respect to x, you first multiply the power of x by the coefficient of x to find ...

This could be happening for two reasons.  

Firstly, the negative form of the expression that you are being asked to integrate could be appearing in your answer, after you've used the 'integrating b...