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(C3) Show that 4csc^2(x) - cot^2(x) = k can be expressed as sec^2(x) = (k-1)/(k-4) where k != 4

The student can answer this in several ways. One using the simple, known identities csc= 1/sin, cot=1/tan, sec=1/cos, tan=sin/cos, sin^2 + cos^2 = 1 and basic algebra is the following: 4csc^2 - cot^2 = k4/si...
FH
Answered by Fearghus H. • Maths tutor
4290 Views

Find the binomial expansion of (-8+4x)^(2/3) up to and including the term in x^2.

The formula booklet is useful for this type of question, but only once we've rearranged the expression into the correct form. The formula booklet expression is: (1 + z)^n = 1 + n z + 0.5 n*(n-1) z^2 + .... T...
DM
Answered by David M. • Maths tutor
4697 Views

y = 2x^3 + 15x^2 + 24x + 10 Find the stationary points on this curve and determine their nature

First differentiate the function to obtain dy/dx = 6x^2 + 30x + 24 Then set this equal to 0 and solve to find the x values of the stationary points 6x^2 + 30x + 24 = 0 6(x^2 + 5x + 4) = 0 6(x +1)(x+4) = 0 th...
KW
Answered by Kate W. • Maths tutor
10618 Views

Show that (1 - cos(2x)) / (1 + cos(2x)) = sec^2(x) - 1

First, take the side of the equation that looks most complicated because it often needs simplifying. This is the LHS in this case. The LHS has cos(2x) twice - therefore the double angle formula probably appl...
LG
Answered by Louis G. • Maths tutor
7315 Views

Integrate 5(x + 2)/(x + 1)(x + 6) with respect to x

This term cannot be integrated in the form that it is in. We will have to do some algebraic manipulation to rewrite it. The term can be split into partial fractions because the denominator of the term has be...
LP
Answered by Lata P. • Maths tutor
3622 Views