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Show that 2cos^2(x) = 2 - 2sin^2(x) and hence solve 2cos^2(x) + 3sin(x) = 3 for 0<x<180

You can rearrange the equation to get 2cos^2(x)+2sin^2(x) = 2. This can be factorised to get cos^2(x) + sin^2(x) = 1 which is a known identity. We can use the fact that 2cos^2(x) = 2sin^2(x) - 2 and substitu...
MR
5610 Views

This is a question from a past paper: https://prnt.sc/r6jnxc

The answer is in the same image as the question.
MS
2414 Views

Simplify fully the expression ( 7x^2 + 14x ) / ( 2x + 4 )

The first thing we try to do is factorise the numerator and denominator. Let's start with the numerator. We can take a 7 out of the bracket to leave us with 7( x 2 + 2x ) on the numerator. But we're not done...
CB
2904 Views

Work out the coordinates for the stationary point of y = x^2 + 3x + 4

dy/dx = 2x + 3dy/dx = 0 at stationary pointTherefore 2x + 3 = 0so x = -3/2so y = (-3/2)^2 +3 (-3/2) + 4so y = 9/4 - 9/2 + 4therefore y = 7/4so the coordinates of the stationary point are (-3/2 , 7/4)
IM
4286 Views

Plot the graph of 1/x for x greater than 0.

This can seem quite tricky at first, so let's break it down into steps. If we draw a table of x values (for example 0, 1, 2, 3, 4), we can put each value into our equation and find a corresponding value of y...
OT
3560 Views