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My first step would be to put all the known values on one side: ln(x) = ln(6) - ln(3) Then, using log laws, we have: ln(x) = ln(6/3) so, ln(x) = ln(2) so, x = 2

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)...