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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...

Answered by Fearghus H. • Maths tutor

3854 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 + nz + 0.5n*(n-1)

Answered by David M. • Maths tutor

4352 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) ...

Answered by Kate W. • Maths tutor

10248 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 a...

Answered by Louis G. • Maths tutor

6872 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...

Answered by Lata P. • Maths tutor

3395 Views