in Quantitative Aptitude recategorized by
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If  $\theta$ is an acute angle and $\tan\theta+\cot\theta =2$, Find the value of $\tan ^{7}\theta +\cot ^{7}\theta$.

  1. $-2$
  2. $1$
  3. $2$
  4. $0$
in Quantitative Aptitude recategorized by
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$\text{Given that : $\tan\theta+\cot\theta=2$}$

$\because$ $\cot\theta=\frac{1}{\tan\theta}$

$\implies$ $\tan\theta+\frac{1}{\tan\theta}=2$

$\implies$ $\frac{tan^2\theta+1}{\tan\theta}=2$

$\implies$ $\tan^2\theta+1=2\tan\theta$

$\implies$ $(\tan\theta-1)^2=0$

$\implies$ $\tan\theta=1$

$\because \tan45^\circ=1$

$\therefore \tan\theta=\tan45^\circ$

$\implies$ $\theta=45^\circ$

$\therefore$ $\tan^7\theta+cot^7\theta=(\tan45^\circ)^7+(\cot45^\circ)^7$

$\because tan45^\circ=cot45^\circ=1$

$\therefore$ $\tan^7\theta+cot^7\theta=1$

$\text{Option B is correct.}$
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