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Noticing that tan(5x) = tan(3x+2x) we use the tan compound angle formula to find tan(5x) = (tan(2x)+tan(3x))/(1-tan(2x)tan(3x)) and thus tan(5x)tan(3x)tan(2x) = tan(5x)-tan(3x)-tan(2x). From then we can i...

A Tierce de Picarie ('Picardy Third') is a surprise major chord at the end of a piece. Whilst the piece is predominantly in a minor mode, the final chord (which will always be the tonic in music of this ...

To factorise and solve this equation we must put it into two brackets, instead of one, each with a single x term. As the is an x^2 term we know there must be an x in each bracket Because the number term a...

Here we have 2 unknown variables, x and y. First number the two equations, so x + 5y = 9 is (1), while 3x + 2y = 5 (2).

Rearrange both equations so that they become (1) x = 9-5y and (2) x= (5-2y)/3...

First of all take the word in the infinitive (e.g. comer/ hablar/ vivir) Then put conjugate it into the first person singular (e.g. como, hablo, vivo). Then take off the "o" ending. If it is an ...