Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the general solution of the following trigonometric equation:

tan squared straight theta space plus space cot squared straight theta space equals space 2




Answer
tan squared straight theta space plus space cot squared straight theta space equals space 2
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#6 {main}</pre>       rightwards double arrow      tan to the power of 4 straight theta space minus space 2 space tan squared straight theta space plus space 1 space equals space 0

rightwards double arrow         left parenthesis tan squared straight theta minus 1 right parenthesis squared space equals space 0             rightwards double arrow        tan squared straight theta space minus 1 space equals space 0

rightwards double arrow          tan squared straight theta space minus space 1 space equals space left parenthesis 1 right parenthesis squared space equals space tan squared straight pi over 4
Using               tan squared straight x space equals space tan squared straight y space rightwards double arrow space straight theta space equals space nπ space plus-or-minus space straight a comma space space straight n space element of space straight Z, we get
                                 straight theta space equals space nπ plus-or-minus straight pi over 4 comma space space straight n space element of space straight Z
Which is the required general solution.

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