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cosec(2x) + cot(2x)

CONVERT ALL COSEC/COT/SEC FUNCTIONS INTO FUNCTIONS USING SIN/TAN/COS

= 1 / (sin2x) + cos(2x) / sin(2x)

COMBINE THE TWO FRACTIONS INTO ONE

= [1...

Initially, we must recognise the simplest way to integrate this equation is using the 'reverse chain rule' method. 

This means raising the value of the power, in this case '3', by one, and then div...

dy/dx = (4 * 3)x^(3-1) + 2x^(2-1)*cos(x²)

         = 12x² + 2xcos(x²) 

If the lines are parallel then when the line AB is given in the form y=mx+c then the gradient m of AB is equal to that of the other line. Rearranging the equation for line AB gives y=-(5/3)x-1 so m=-(5/3)...

For this example it would be better to use a dummy variable (a variable just to help with solving the equation but isn't a part of the final answer). Let us say our dummy variable, t = 1+x^2. So, substitu...