Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the general solution of the following trigonometric equation:

tan space straight x space plus space tan space 2 straight x space plus space tan space straight x space tan space 2 straight x space equals space 1



Answer
tan space straight x space plus space tan space 2 straight x space plus space tan space straight x space tan space 2 straight x space equals space 1

rightwards double arrow       tan space straight x space plus space tan space 2 straight x space minus space 1 space minus space tan space straight x space tan space 2 straight x space space        rightwards double arrow fraction numerator tan space straight x space plus space tan space 2 straight x over denominator 1 minus tan space straight x space tan space 2 straight x end fraction space equals space 1

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#6 {main}</pre>                               open square brackets Using space fraction numerator tanA plus tanB over denominator 1 minus tanA space tanB end fraction space equals space tan left parenthesis straight A plus straight B right parenthesis close square brackets

rightwards double arrow                tan space 3 straight x space equals space 1 space equals space tan space 45 degree space equals space tan straight pi over 4 space space space space space space rightwards double arrow space space space space space space 3 straight x space equals space nπ space plus space straight pi over 4 comma space space straight n space element of space straight Z
rightwards double arrow                            straight x space equals space nπ over 3 plus straight pi over 12 comma space straight n space element of space straight Z
Which is the required general solution.

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