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Rearrange the equation to give sin3θ=(sqrt3)cos3θ, then divide through by cos3θ to give sin3θ/cos3θ=sqrt3. We know from our trig identities that sinx/cosx=tanx, so our equation now becomes tan3θ=sqrt3. Us...

To start off with let 2/P(P-2)=A/P + B/(P-2) making the RHS of the equation one fraction gives : (A(P-2)+B(P))/P(P-2). So now we can compare the numerators (as the denominators are the same): A(P-2)+B(P)=...

If line L is parallel to line A it will have the same gradient; in this case, the letter a in the equation y=ax+b represents the gradient. Therefore line L will be of the form y=4x+b. To find the value of...

 ∫(21x⁶-e^2x-1/x+6)dx

To tackle this question, I would do each part separately.

Firstly, take 21x⁶...using the product rule this intergrates ...

To differentiate this equation, treat it like you would any other equation you are differentiating without exponentials i.e. take each term on it's own and differentiate that individually, then put the an...