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Welcome to NRICH.

Manipulating trig expressions

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By Anonymous on Monday, April 30, 2001 - 12:51 am:

Please help with this problem:

Eliminate x and y from the equations:
cos x + cos y = a
sin x + sin y = b
sin 2x + sin 2y=c

Thanks!!!

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By Kerwin Hui (Kwkh2) on Monday, April 30, 2001 - 06:05 pm:

Anonymous,

cos x + cos y = a ... (1)
sin x + sin y = b ... (2)
sin 2x + sin 2y = c ... (3)

(1)×(2) : ½(sin 2x + sin 2y)+ sin (x+y)=ab
so sin (x+y) = ab-½c.

(1)²+(2)² : 2 + 2 cos x cos y + 2 sin x sin y = a²+b²
i.e. a²+b²-1 = 2 cos (x-y)

Now substitute in

sin 2x + sin 2y = 2 sin (x+y) cos(x-y)

Kerwin

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