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The most general solution of \tan \theta=-1\:\:and\:\:\cos\theta=\frac{1}{\sqrt2} is

Option: 1

n\pi + \frac{{7\pi }}{4}


Option: 2

n\pi + {( - 1)^n}\frac{{7\pi }}{4}


Option: 3

2n\pi + \frac{{7\pi }}{4}


Option: 4

None of these


Answers (1)

best_answer

 \\\tan\theta = - 1\;\; \Rightarrow \;\;\theta = \frac{3\pi }{4}\;,\;\frac{7\pi}{4} \\ \cos \theta = \frac{1}{\sqrt 2}\;\; \Rightarrow \;\;\theta = \frac{\pi }{4}\;,\;\frac{7\pi }{4}\\ Common\;\;\theta = \frac{7\pi }{4}\;\;\\ \text{As both cos and tan functions repeat after an interval of 2}\pi\text{, so} \\General\,\,solution = 2n\pi + \frac{{7\pi }}{4}

 

Posted by

Rakesh

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