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.

Answered by Daniel M. Maths tutor

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