Find all exact solutions that exist on the interval [0, 2π). 1 − 2 tan(ω) = tan2(ω) w =

A possible solution: First add 1 to both sides and reduce the RHS via the Pytagorean identity.

Rewrite and in terms of and :

Multiply both sides by :

Use the double angle identities:

Divide both sides by :

Now, for , or , where is any integer. will fall in the interval for , which means we have

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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