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Can you please rephrase the question because I can't see the question in that line.

Brilliant. But how did you know to divide the denominator like that because it is not reducible. (1st line I mean)

Can someone show me where to go next. I've done a question up to here. \frac{1}{2}\int_{0}^{1}\frac{1-t^2}{t^4+t^2+1} I've been using t=tanx/2 and I'm trying to prove for 1/4ln3. If it's impossible from here, please tell me.

Thanks. I got another one here. I've tried so hard but I can't seem to get the answer which is 7. \int_{3}^{8}\frac{x}{(x+1)-\sqrt{x+1}}dx I've been using the substitution u^2 = x+1

Can somebody help me with this one. \int \frac{dx}{(4+x^2)^\frac{3}{2}} using x=2tan\theta

Show: 2sin^{-1}\frac{3}{5}=sin^{-1}\frac{24}{25} and sin^{-1}\frac{3}{5}+tan^{-1}\frac{7}{24}=cos^{-1}\frac{3}{5} I have no idea where to start in both of them except for drawing triangles.

Use the angle bisector theorm

Why does cos3@=1/2 ?

Yeah I already know about that part. But it's the actually solution I don't know how to get.

The Cmbridge book does not explain properly. Can someone guide me through the steps. cos3\Theta=4cos^3\Theta -3cos\Theta Solve for 8x^3-6x-1=0

Got another question from Cambridge that I'm stuck on. PS. I looked at the solutions, but I still don't get it. I need someone to explain it to me step by step. P(x) is a monic polynomial of degree 4 with integer coefficients and constant term 4. One zero is root2, another zero is rational and...

Could you please explain this.

I know this may seem like a simple question, but... For P(x)=2x^3-3x^2+2x-3 You are told that it has a rational root. The answer says its 3/2 but how can you do this using the factor theorem?

4x^3+12x^2-15x+4 You are given that the polynomial has a double root. Find all the roots using the idea of multiplicity of roots.

Hi. I got a question here is can't seem to solve. Tangents at P(x_1,y_1) and Q(x_2,y_2) from the curve x^2=4ay intersect at M(\frac{2a(y_2-y_1)}{x_2-x_1},\frac{x_1y_2-x_2y_1}{x_2-x_1}) Using x_1^2=4ay_1 \and\ x_2^2=4ay_2, show M is (\frac{x_1+x_2}{2},\frac{x_1x_2}{4a}) I've got the...

Can someone help m with Question 10(d) in Exercise 9D of the cambridge 3U year 11 book. i) The line P_{1}P_2 intersects the parabola x^2=4ay. Obtain an equation whose roots are the values of \lambda corresponding to the points of intersection (P_{1}P_2 is divided in the ratio \lambda:1)...

x=3+rcox@ and y=-2+rsin@ If @ is constant and r is variable Source: Cambridge Maths 3 Unit Year 11

x+iy=(a+ib)^2 |x+iy|=|(a+ib)^2| |x+iy|=|a+ib|^2 \sqrt{x^2+y^2}=a^2+b^2 \therefore x^2+y^2=(a^2+b^2)^2

Anyone?

Hi. I got 2 questions which I'm stuck on. 1) The tangent and normal at any point P on an ellipse meet the major axis at T and G respectively. If PN is the ordinate of P and C the centre, prove that CT.NG=b^2 2) P is a point on the ellipse \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 with centre O. A...