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How do I remember the trigonometry identities from C3 in the exam?

I often find it difficult to remember all the different identities, so what is useful is instead to just remember the familiar identity sin^2(x) + cos^2(x) = 1 that we have come across many times, and divide...
JS
Answered by Joshua S. • Maths tutor
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Differentiate with respect to x: y=xln(x)

Recall the product rule for differentiation. If y=uv, where u and v are functions defined by functions of x, then we can take the derivative of y as: y'=u'v+v'u ( ) (where ' denotes the derivative) Applying ...
GP
Answered by George P. • Maths tutor
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Show that the integral ∫(1-2 sin^2⁡x)/(1+2sinxcosx) dx = (1/2) ln2 between the limits π/4 and 0. [5 marks]

First, we use the trig identities: cos2x=cos^2x-sin^2x, cos^2x+sin^2x=1 and sin2x=2sinxcosx to transform the integral to ∫(cos2x)/(1+sin2x)dx. We know that ∫f'(x)/f(x)dx = ln|f(x)|+c, so we let f(x)=1+sin2x....
AC
Answered by Abby C. • Maths tutor
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(4-2x)/(2x+1)(x+1)(x+3) = A/(2x+1)+B/(x+1)+C(x+3) Find the values of the constants A, B and C

First, multiply throughout by the denominator of the main function to give as follows: 4-2x = A(x+1)(x+3) + B(2x+1)(x+3) + C(2x+1)(x+1) Then, choose values of x which will cause two of the constants to vanis...
MC
Answered by Michael C. • Maths tutor
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Edexcel C1 2015 Q10. A curve with equation y = f (x) passes through the point (4, 9). Given that f′(x)=3x^(1/2)-9/(4x^(1/2))+2. Find f(x), giving each term in its simplest form.

I would go through a similar example of integration with the student using the whiteboard and would explain the use of integration, and would then get them to do the above question, giving them hints when ne...
IA
Answered by Issy A. • Maths tutor
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