Find the values of A between and including 0 and 360 degrees for tan(2A) = 3tan(A)
You cannot work with this equation in the current form so you must use identities to find an equivalent form that you can work with. It is known that tan(2A) = 2tan(A) / 1-tan2(A) so set this equal to 3tan(A), multiply the denominator to the other side and with some rearrangement you will get 3tan3(A) - tan(A) = 0. Now it should hopefully be clear that you can factorise out tan(A) and you will get two solutions of tan(A) = 0 and 3tan2(A) - 1 = 0. The second term equates to tan(A) = +and- (1/3)0.5. The final step is to sketch a graph of y = tan(A) and using that with the inverse tan function on your calculator you should get the desired values within the required range as 0o, 180o, 360o, 30o, 210o, 150o, 330o.
DM
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