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Using the definitions of hyperbolic functions in terms of exponentials show that sech^2(x) = 1-tanh^2(x)

tanh(x) = ((e^x-e^-x)/2)/((e^x+e^-x)/2) 1 - tanh²(x) = 1-((e^x-e^-x)/(e^x+e^-x))² = ((e^2x+...

Answered by Chris B. • Further Mathematics tutor

6297 Views

Core 3: Find all the solutions of 2cos(2x) = 1-2sin(x) in the interval 0<x<360

2cos(2x) = 1-2sin(x)

2(1-2sin²(x)) = 1-2sin(x) -- by our trigonometric functions

2-4sin²(x) = 1-2sin(x)

4sin²(x)-2sin(x)-1=0 -- rearrange

sin(x...

Answered by Chris B. • Maths tutor

8578 Views

x^3 + 2x^2 - 9x - 18 = (x^2 - a^2)(x + b) where a,b are integers. Work out the three linear factors of x^3 + 2x^2 - 9x - 18. (Note: x^3 indicates x cubed and x^2 indicates x squared).

There are a few different ways to approach this problem. The most obvious is to attempt to factorise x³+ 2x²- 9x - 18. However it is very difficult to approach the problem like thi...

Answered by Chris B. • Further Mathematics tutor

4356 Views

Jo has the following 9 coins in her purse: 10p, 2p, 2p, 50p, 10p, 1p, 20p, 2p, 2p. Work out the median, mean, mode and range.

To work out the median of a set of numbers we first place them in order:

1p, 2p, 2p, 2p, 2p, 10p, 10p, 20p, 50p

Then the median is the middle value in the list, in this case 2p.

To wo...

Answered by Chris B. • Maths tutor

5367 Views

Briefly describe the use of Law reports and their importance.

The importance of Law reports within the English Judicial System stem from a variety of interlinking factors, primarily that a core principle of the Legal System is that “the Law is for all” and thus shou...

Answered by Lewis S. • Law tutor

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