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in Trigonometry by (53.1k points)

Find the set of values of x for which (tan3x - tan2x)/(1 + tan3x tan2x) = 1

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The first equation can be written as

when sin 1/2(x + y) = 0 we have that either sin 1/2 x = 0 or sin 1/2 y = 0.Therefore, either sin 1/2(x + y) = 0 or cos 1/2(x + y) = 0.

⇒ x + y  = 0, or x  = 0 or y = 0.  As |x| + |y| = 1, therefore when x + y = 0, we have to reject x + y = 1, or x + y = -1 and solve it with x − y = 1 or x - y = -1 which gives (1/2,-1/2) or (-1/2,1/2) as the possible solution. Again solving with x = 0, we get (± 1,0), and solving with y = 0, we get (±1 ,0) as the other solution. Thus, we have six pairs of solution for x and y.

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