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Using the equation cos(a+b) = cos(a)cos(b) - sin(a)sin(b) or otherwise, show that cos(2x) = 2cos^2(x) - 1.

First let a = b = x such that: cos(a + b) = cos(a)cos(b) - sin(a)sin(b) becomes: cos(x + x) = cos(x)cos(x) - sin(x)sin(x) Leading to: cos(2x) = cos 2 (x) - sin 2 (x) Using the fact that sin 2 (y) + cos 2 (y)...
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Answered by Benjamin H. • Maths tutor
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Give the definition simple harmonic motion and write down the defining equation for such motion stating the meaning of any symbols involved.

Simple harmonic motion is defined as a form of periodic motion in which a point or body oscillates in such a way that the acceleration of the point or body is directly proportional to its displacement from t...
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Answered by Benjamin H. • Physics tutor
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Explore the ways in which Yeats presents his journey in ‘Sailing to Byzantium’

Yeats wrote of Byzantium, “I symbolise the search for the spiritual life by a journey to that city”[1], and indeed, his poem reflects this quest for some form of religion. From a foundation in Christianity, ...
HK
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What is the best way to plan an essay?

When answering an essay question, the most important stage, in my view, is the planning. Personally, I like to make a mind map, but it really depends on what you feel the most comfortable with, and I recomme...
EO
Answered by Emma O. • History tutor
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Why is the argument of a+bi equal to arctan(b/a)?

Think about the point a+bi on the complex plane. Specifically, a is how far along the x (real) axis, and b is how far up the y (imaginary) axis the point is. If you draw a line connecting the origin and the ...
MS
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