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The most general solution of the equations $\tan \theta = -1 , \cos \theta = 1/ \sqrt 2$ is
Option: 1
$n \pi + 7\pi /4$

Option: 2
$n \pi +(-1)^n \: \: 7\pi /4$

Option: 3
$2n \pi + 7\pi /4$

Option: 4
none

Answers (1)

best_answer

As we have learnt in

General Solution of Trigonometric Ratios -

$\cos \Theta = \cos \alpha$

$\Theta = 2n\pi \pm \alpha , n\epsilon I$

- wherein

$\alpha$ is the given angle

General Solution of Trigonometric Ratios -

$\tan \Theta = \tan \alpha$

$\Theta = n\pi + \alpha , n\epsilon I$

- wherein

$\alpha$ is the given angle

We have $\tan \theta = -1 \: \: and \: \: \cos \theta = 1/ \sqrt 2$

The value of $\theta$ lying between $3 \pi /2 \: \: and \: \: 2 \pi$ and satisfying these two is $7\pi /4$ . Therefore the most general solution is $\theta = 2n \pi + 7 \pi /4$ where n $\epsilon$ Z.

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