Transforming $\tan{\phi} = c_1 \tan{\phi_1}+ c_2 \tan{\phi_2}$ into the form $\phi = d_1 \phi_1 + d_2 \phi_2$

by Aditya Srivastava   Last Updated September 21, 2018 14:20 PM

my problem is that I am trying to transform this trigonometric expression: $$\tan{\phi} = c_1 \tan{\phi_1}+ c_2 \tan{\phi_2}$$

to the form: $$\phi = d_1 \phi_1 + d_2 \phi_2$$

My basic aim is to represent $c_1$ as $f_1(d_1,d_2$) and $c_2$ as $f_2(d_1,d_2)$ by comparing the coefficients. I would be really grateful if someone could help me out with this. Also if someone could suggest someother method for this function estimation, that could also be of great help. Thanks in advance.



Answers 1


If i understand right, you can write

$$\frac{\tan(\phi_1)}{c_1^2+c_2^2}+\frac{c_2}{c_1^2+c_2^2}\tan(\phi_2)$$

Dr. Sonnhard Graubner
Dr. Sonnhard Graubner
September 21, 2018 14:05 PM

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